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In triangle A B C, A B = x, B C = 16. \angle B A C = 97 degrees and \angle A C B = 21 degrees. Find x. Round to the nearest tenth.
Choices:
A:5.8
B:6.5
C:14.2
D:44.3 | A |
|
Two triangles G J I and G K H are similar with a shared vertex G. K H and J I are parallel. Find K J if G J = 8, G H = 12, and H I = 4.
Choices:
A:2
B:4
C:6
D:8 | A |
|
\triangle R S T \cong \triangle A B C. \angle R S T = \angle C B A. S T = 2y - 8, and C B = y + 13. Find x.
Choices:
A:8
B:10
C:13
D:21 | B |
|
\triangle R S V \cong \triangle T V S, and they share a side S V. S V is perpendicular to S R and \angle R V S = 78 degrees. Find x.
Choices:
A:11
B:11.5
C:12
D:12.5 | C |
|
There are four rays B A, B D, B F, and B C with a shared starting point B. \overrightarrow B A and \overrightarrow B C are opposite rays and \overrightarrow B D bisects \angle A B F. If m \angle F B C = 2 x + 25 and m \angle A B F = 10 x - 1, find m \angle D B F.
Choices:
A:25.5
B:50
C:54
D:64.5 | D |
|
There is a right triangle V X W, the hypotenuse V X is 75, and V W = 72, X W = 21. Express the ratio of \cos X as a decimal to the nearest hundredth.
Choices:
A:0.28
B:0.29
C:0.96
D:3.43 | A |
|
In \odot C, point R, M, N, L are on the circle, and M L is the diameter. \angle M C R = x - 1 degrees and \angle R C L = 3x + 5 degrees. Find m \angle R C M.
Choices:
A:27
B:43
C:47
D:67 | B |
|
A B \perp D C and G H \perp F E. A C = 4.4, G H = 3.15, and G E = 6.3. If \triangle A C D \sim \triangle G E F, find A B.
Choices:
A:2.2
B:3.6
C:4.4
D:6.3 | A |
|
Find x for the equilateral triangle R S T if R S = x + 9, S T = 2 x, and R T = 3 x - 9.
Choices:
A:3
B:6
C:9
D:12 | C |
|
Two triangles A E B and A D C are similar with a shared vertex A. E B and D C are parallel. Find x if A E = 3, A B = 2, B C = 6, and E D = 2 x - 3.
Choices:
A:5
B:6
C:8
D:9 | B |
|
In \odot Z, points V, U, Y, X, W are on the circle. \angle W Z X \cong \angle X Z Y, m \angle V Z U = 4 x, m \angle U Z Y = 2 x + 24, and V Y and W U are diameters. Find m \widehat W U X.
Choices:
A:52
B:104
C:154
D:308 | D |
|
Two triangles have a shared vertex with three annotated points A, B, and C. Find the measure of \angle 2 if A B \perp B C.
Choices:
A:64
B:68
C:72
D:76 | B |
|
Find the area of the circle with a diameter 6.2 cm. Round to the nearest tenth.
Choices:
A:19.5
B:30.2
C:60.4
D:120.8 | B |
|
In trapezoid J K L M, J K is parallel to M L. J M = 6, K L = 6, and \angle J M L is 80 degrees. Find m \angle K.
Choices:
A:6
B:60
C:100
D:180 | C |
|
Find the perimeter of the isosceles triangle in yellow with a base length 3.5 ft. Round to the nearest hundredth.
Choices:
A:5.84
B:6.65
C:8.21
D:8.73 | D |
|
Two triangles A E B and A D C are similar with a shared vertex A. E B \parallel D C. A B = x - 2 and B C = 5. Find x.
Choices:
A:5
B:7.5
C:9.5
D:10 | C |
|
In \odot F, B, C, D, A are on the circle and A C is a diameter. \angle C F D is 4 a - 1 degrees. Find the measure of \angle A F B.
Choices:
A:72
B:108
C:120
D:144 | B |
|
The figure shows three parallel horizontal lines, with a diagonal line running through them on the left and a vertical line on the right. The diagonal line on the left intersects with three horizontal lines, with a length of 2x+6 for the lower section and 20-5x for the upper section. The vertical line on the right intersects with three horizontal lines, with a length of y for the upper section and 3/5y+2 for the lower section. The two short line segments cut by the left line are of equal length, and the two short line segments cut by the right line are of equal lengthFind y.
Choices:
A:3
B:4.5
C:5
D:6 | C |
|
The diagonal length of the blue quadrilateral is 8yd, the diagonal length of the green quadrilateral is 4yd, and the area of the blue quadrilateral is 36yd ^ 2. For the pair of similar figures, find the area of the green figure.
Choices:
A:9
B:18
C:72
D:144 | A |
|
The figure shows a quadrilateral ABCD, with S on AC and T on BD. For trapezoid A B C D, S and T are midpoints of the legs. If A B = x + 4, C D = 3 x + 2, and S T = 9, find A B.
Choices:
A:3
B:5
C:7
D:9 | C |
|
The figure shows a \parallelogram ABCD, with BD connected, BD perpendicular to AB, and BD also perpendicular to DC. The length of BD is 6m, and the length of AD is 10m. What is the area of \parallelogram ABCD?
Choices:
A:24
B:30
C:48
D:60 | C |
|
QM is perpendicular to MN, QP is perpendicular to NP, the length of MQ is 2x+2, and the length of QP is 4x-8, NQ is the angular bisector of angle MNP. Find Q M.
Choices:
A:4
B:8
C:12
D:16 | C |
|
The diagram is a quadrilateral with intersecting diagonals and perpendicular to each other. Where AB=AD, BC=DC, and the length from D to the diagonal intersection point is 5, and the length from C to the diagonal intersection point is 12. Find B C.
Choices:
A:5
B:9
C:12
D:13 | D |
|
The figure shows a regular octagon, with a distance of 6cm from the vertex of the central path of the octagon. Find the area of the regular polygon figure. Round to the nearest tenth.
Choices:
A:12.7
B:25.5
C:101.8
D:203.6 | C |
|
As shown in the figure, the parallelogram with 2sides of 13yd and 10yd respectively. Find the area of the parallelogram. Round to the nearest tenth if necessary.
Choices:
A:65
B:91.9
C:112.6
D:130 | B |
|
The diagram shows a triangle with a perpendicular length of 7ft and base length is 10.2ft. Find the area of the figure. Round to the nearest tenth if necessary.
Choices:
A:35.7
B:49
C:71.4
D:104.0 | A |
|
During a rescue search, a helicopter flew b kilometres west from point X to point Y, then changed course and flew 10.7 kilometres north to point Z. If point Z is on a bearing of 335° T from point X:
Now, if the distance that the helicopter must fly between point Z and point X is d kilometres, calculate d to one decimal place. | 11.8 |
|
Three television presenters are practising their navigation skills before heading off on an expedition to a remote location. Amelia at point B is positioned 17.6 metres south of Ned at point A. Bart at point C is due east of Amelia and on a bearing of S 38^\circ E from Ned. If Ned and Bart are d metres apart, find d to one decimal place. | 22.3 |
|
In remote locations, photographers must keep track of their position from their base. One morning a photographer sets out from base, represented by point B, to the edge of an ice shelf at point S on a bearing of 055°. She then walked on a bearing of 145° to point P, which is 916 metres due east of base.
If the photographer were to walk back to her base from point P, what is the total distance she would have travelled? Round your answer to one decimal place. | 2191.7 metres |
|
A rally car starts at point P and races 191 kilometres south to point Q. Here the car turns west and races for 83 kilometres to point R. At point R the car must turn to head directly back to point P.
What is the compass bearing of R from P? Give your answer to one decimal place. | S 23.5 ^\circ W |
|
Consider the points on the diagram P, A and N where N denotes the north cardinal point. Angle PAN is 45°.
Using the diagram, find the true bearing of P from A. | 315^\circT |
|
Consider the points on the diagram P, M and S where S denotes the south cardinal point. Angle PMS is 50°.
Using the diagram, find the true bearing of P from M. | 230 ^\circ T |
|
Consider the points on the diagram P, M and S where S denotes the south cardinal point. Angle PMS is 37°.
Using the diagram, find the true bearing of P from M. | 217 ^\circ T |
|
Consider the point A. The angle between line OA and the positive direction of the x-axis is 28°.
Find the true bearing of A from O. | 118掳T |
|
Consider the point A. The angle between line OA and the south direction is 32°.
What is the true bearing of A from O? | 212°T |
|
Consider the point A. The angle between line OA and the north direction is 31°.
Find the true bearing of point A from O. | 329° T |
|
In the figure above, triangle ABC formed by the dashed line, angle A is 37° and angle B is 48°. Find the true bearing of point A from point B. | 270 ^\circ T |
|
In the figure below, point B is due East of point A. We want to find the position of point A relative to point C. Triangle ABC formed by the dashed line, angle A is 49° and angle B is 39°.
Find the true bearing of point A from point C. | 319 ^\circ T |
|
In the figure below, point B is due East of point A. Triangle ABC formed by the dashed line, angle A is 49° and angle B is 41°. Find the true bearing of point B from point A.
Choice:
A. 090^\circ T
B. 180^\circ T
C. 049^\circ T
D. 041^\circ T | 090^\circ T |
|
Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 49° and angle B is 41°.
Find the true bearing of point B from point C.
Choice:
A. 053 ^\circ T
B. 082 ^\circ T
C. 045 ^\circ T
D. 037 ^\circ T | 053 ^\circ T |
|
Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 42° and angle B is 53°.
Find the true bearing of point C from point A. | 132 ^\circT |
|
Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 38° and angle B is 49°.
Find the true bearing of point C from point B. | 221 ^\circ T |
|
Given the diagram shown, if the bearing of the clearing from the town is a°. Starting from town, heading 3.2 kilometers due north and then 5.9 kilometers due east is clearing. Find a to the nearest degree. | 62^\circ |
|
At a point during the flight, a plane is 42 kilometres south and 57 kilometres west of the airport it left from.
Find the size of the angle marked b to one decimal place. | 53.6^\circ |
|
Luke sailed for 116 kilometres on a bearing of 231^\circ .
If w is how many kilometres west he has sailed from his starting point, find $w$ to one decimal place. | 90.1 |
|
Considering the diagram below, find x, the angle of elevation to point A from point C. The picture shows a right angled triangle with a base length of 25 and a height of 19.
Round your answer to two decimal places. | 37.23 |
|
Sally measures the angle of elevation to the top of a tree from a point $20$m away to be 43^\circ . If the height of the tree is H m, find the value of H.
Round your answer to the nearest whole number. | 19 |
|
A helicopter is flying at an altitude of 198 metres, at an angle of depression of 44° to its landing pad. What is the distance d between the helicopter and the landing pad?
Round your answer to the nearest whole number. | 285 |
|
Considering the diagram below, ABCD is a rectangle, find x, the angle of depression from point B to point C. The lengths of AC and BC are 3 and 5, respectively.
Round your answer to two decimal places. | 53.13 |
|
A fighter jet, flying at an altitude of 2000 m is approaching a target. At a particular time the pilot measures the angle of depression to the target to be 13^\circ . After a minute, the pilot measures the angle of depression again and finds it to be 16^\circ .
Now find the distance covered by the jet in one minute.
Round your answer to the nearest meter. | 1688 |
|
A man stands at point A looking at the top of two poles. Pole 1 has height 8 m and angle of elevation 34^\circ and Pole 2 has height 25 m and angle of elevation 57^\circ . The man wishes to find the distance between the two poles.
Hence find BC, the distance between the two poles in metres.
Round your answer to one decimal place. | 4.4 m |
|
From the cockpit of an aeroplane flying at an altitude of 3000 m, the angle of depression to the airport is 57°. The aeroplane continues to fly in the same straight line, and after a few minutes the angle of depression to the airport becomes 67°.
Now find the distance between the two sightings.
Round your answer to the nearest metre. | 675 m |
|
An airplane is currently flying 35^\circ south of east, as shown in the image.
The control tower orders the plane to change course by turning 7^\circ to the left. How many degrees south of east is the new course that the plane is ordered to fly? | 28 |
|
In triangle ABD, BC is the perpendicular to AD, with AB length of 32 and BD length of 35. Angle A is 50°, angle D is 45°. Consider the following diagram. Hence, find the length of AD correct to two decimal places. | 45.32 |
|
In triangle ABD, BC is the perpendicular to AD, with AB length of 58 and BD length of 72. Angle A is 57°, angle D is 31°. Consider the following diagram. Hence, find AD correct to two decimal places. | 93.31 |
|
In triangle ABC, angle A is 60°, angle B is 35°, and the length of the perpendicular CD of AB is 9. Consider the following diagram.Hence, find the length of AB correct to two decimal places. | 18.05 |
|
The quadrilateral ABCD in the figure is composed of two right angled triangles ABC and ACD, angle B is 35°, angle BCD is a right angle, the length of BC is 13. Consider the following diagram:Find the size of \angle ACD. | 35掳 |
|
Consider the following diagram. The height of the dashed line in the figure is 68. The angle enclosed by the blue arc is 46°, and the angle enclosed by the red arc is 37°. Hence, use the rounded values of y and w to find x, correct to 1 decimal place. | 24.6 |
|
Consider the following diagram. The height of the rectangle in the picture is 63, the angle enclosed by the purple arc is 67° and the angle pointed by the arrow is 39°. Hence, find x, correct to one decimal place. | 51.1 |
|
In the following diagram, \angle CAE=61^\circ , \angle CBE=73^\circ and CE=25.
Find the length of BD, correct to one decimal place. | 6.3 |
|
A safety fence is constructed to protect tourists from the danger of an eroding castle toppling down. At point A, the surveyor takes an angle measurement to the top of the tower of 10°. She then walks 29 meters towards the tower and takes another reading of 22° at point B.
Hence or otherwise, find the value of h to the nearest metre. | 9 |
|
The final approach of an aeroplane when landing requires the pilot to adjust their angle of descent to about 3°. If the plane is 12 metres above the runway and has d metres until touchdown, find d to the nearest metre. | 229 |
|
Two flag posts of height 13 m and 18 m are erected 21 m apart. Find l, the length of the string (in metres) needed to join the tops of the two posts, correct to one decimal place. | 21.6 |
|
A suspension bridge is being built. The top of the concrete tower is 35.5 metres above the bridge and the connection point for the main cable is 65.9 metres from the tower.
Assume that the concrete tower and the bridge are perpendicular to each other.
If the length of the cable is h metres, find h to two decimal places. | 74.85 |
|
The airtraffic controller is communicating with a plane in flight approaching an airport for landing. The plane is 10369 metres above the ground and is still 23444 metres from the runway. If \theta ° is the angle at which the plane should approach, find \theta to one decimal place. | 23.9 |
|
A ship is 27m away from the bottom of a cliff. A lighthouse is located at the top of the cliff. The ship's distance is 34m from the bottom of the lighthouse and 37m from the top of the lighthouse.
Hence find the height of the lighthouse to the nearest tenth of a metre. | 4.6 m |
|
Sand has an angle of friction of about 40°. This means once it gets over this it slides down the side of the sand pile. Mae is getting a delivery of sand to her home, but the area where the sand will be delivered is only 10.6 metres wide. If h metres is the maximum height of the sandpile, find h to one decimal place. | 4.4 |
|
A farmer wants to build a fence around the entire perimeter of his land, as shown in the diagram. The fencing costs £37 per metre. the lengths of EF and CD are x metre and y metre.
At £37 per metre of fencing, how much will it cost him to build the fence along the entire perimeter of the land? | 777 |
|
In a right angled triangle ABC, angle A is 30°, angle B is 60°, the length of AB is sqrt{3}, and the length of BC is h. Find the length of side h. | 1 |
|
In the right angled triangle, a marked right angled line has a length of 4 and a slanted line has a length of 4*sqrt{2}. Consider the adjacent figure:
Solve for the unknown \theta . Leave your answer in degrees. | 45^\circ |
|
In the right angled triangle, the marked angle is 60°, the marked right angled side has a length of 11, and the diagonal side has a length of w. Consider the adjacent figure:
Solve for the unknown w. | 22 |
|
In the right angled triangle, the marked angle is \theta, the marked right angled side has a length of 12, and the diagonal side has a length of 8*sqrt{3}. Consider the adjacent figure:
Solve for the unknown \theta . Leave your answer in degrees. | 60^\circ |
|
In the right angled triangle, the marked angle is 30°, the marked right angled side has a length of 8.5, and the diagonal side has a length of P. Consider the adjacent figure:
Solve for the unknown P. | 17 |
|
In the right angled triangle, the marked angle is 30°, the marked right angled side has a length of x, and the diagonal side has a length of sqrt{10}. Consider the adjacent figure:
Solve for the exact value of x. | \frac{\sqrt{30}}{2} |
|
In the right angled triangle, the marked angle is 45°, the lengths of the two right angled edges are 4*sqrt{3} and y respectively, and the diagonal side has a length of x. Consider the adjacent figure:
Solve for the exact value of x. | 4\sqrt{6} |
|
In this right-angled triangle, one of the acute angles measures 45^\circ, one leg measuring 4\sqrt{3}. Consider the adjacent figure:Solve for the exact value of y. | 4\sqrt{3} |
|
In this right-angled triangle, one of the acute angles measures 60^\circ, the hypotenuse measures 9. Consider the adjacent figure:
Solve for the unknown a. | \frac{9\sqrt{3}}{2} |
|
In this right-angled triangle, one of the acute angles measures 60^\circ, the hypotenuse measures 8\sqrt{5}. Consider the adjacent figure:Find the exact value of y. | 4\sqrt{5} |
|
A right trapezoid, with one of its base angles measuring 30^\circ, has an adjacent leg length of 8 to this angle. The length of the shorter base of the trapezoid is 4. Find t. | 4+4\sqrt{3} |
|
In this right-angled triangle, one of the acute angles measures 60^\circ, one leg measuring \sqrt{3}. Find the length of side h. | 1 |
|
In this right-angled triangle, one of the acute angles measures 60^\circ, one leg measuring 11. Solve for the unknown w. | 22 |
|
In this right-angled triangle, one leg measuring 12, the hypotenuse measures 8\sqrt{3}. Solve for the unknown \theta . Leave your answer in degrees. | 60^\circ |
|
In this right-angled triangle, one of the acute angles measures 60^\circ, one leg measuring \sqrt{3}. Find the length of side x, leaving your answer as an exact value. | 2 |
|
In this right-angled triangle, one of the acute angles measures 30^\circ, one leg measuring 8.5. Consider the adjacent figure:
Solve for the unknown P. | 17 |
|
In this right-angled triangle, one of the acute angles measures 30^\circ, one leg measuring \sqrt{10}.Consider the adjacent figure:
Solve for the exact value of x. | \frac{\sqrt{30}}{2} |
|
In this right-angled triangle, one of the acute angles measures 45^\circ, one leg measuring 4\sqrt{3}. Consider the adjacent figure:
Solve for the exact value of x. | 4\sqrt{6} |
|
A circle with a radius of $8 \mathrm{~cm}$. Find the circumference of the circle shown, correct to two decimal places. | Circumference $=50.27 \mathrm{~cm}$ |
|
A circle with a radius of $18 \mathrm{~cm}$. Find the circumference of the circle shown, correct to one decimal place. | Circumference $=113.1 \mathrm{~cm}$ |
|
A circle with a diameter of $13 \mathrm{~cm}$. Find the circumference of the circle shown, correct to two decimal places. | $C=40.84 \mathrm{~cm}$ |
|
A circle with a circumference of $44 \mathrm{~cm}$. Consider the circle below.
What is the radius $r$ of the circle?
Round your answer to two decimal places. | $$r=7.00$$ |
|
A circle with a circumference of $42 \mathrm{~cm}$. Consider the circle below.
What is the diameter $D$ of the circle?
Round your answer to two decimal places. | $D=13.37$ |
|
The radius of a quarter circle is $10 \mathrm{~mm}$. Calculate the total perimeter of the following figure, correct to one decimal place. | Perimeter $=35.7 \mathrm{~mm}$ |
|
A circle with a radius of $6 \mathrm{~cm}$. Find the area of the circle shown, correct to one decimal place. | Area $=113.1 \mathrm{~cm}^{2}$ |
|
The radius of the following figure is $2 \mathrm{~cm}$. Calculate the area of the following figure, correct to one decimal place. | Area $=9.4 \mathrm{~cm}^{2}$ |
|
A circle with a radius of $3 \mathrm{~cm}$. Find the exact area of the circle shown.
Give your answer as an exact value in terms of $\pi $. | Area $=9 \pi \mathrm{cm}^{2}$ |
|
A circle with a radius of $11 \mathrm{~cm}$. Find the area of the circle shown.
Give your answer as an exact value. | Area $=121 \pi \mathrm{cm}^{2}$ |
|
A circle with a radius of $50 \mathrm{~cm}$. Find the area of the circle shown.
Give your answer as an exact value. | Area $=2500 \pi \mathrm{cm}^{2}$ |
|
A circle with a radius of $ \frac{1}{5} \mathrm{~cm}$. Find the area of the circle shown.
Give your answer as an exact value. | Area $=\frac{\pi}{25} \mathrm{~cm}^{2}$ |
|
A figure with a radius of $ 5 \mathrm{~mm}$. Find the exact area of the given figure: | Area $=\frac{25 \pi}{4} \mathrm{~mm}^{2}$ |
|
A figure with a radius of $ 11 \mathrm{~m}$. Find the area of the shape shown.
Give your answer as an exact value. | Area $=\frac{121 \pi}{4} \mathrm{~m}^{2}$ |
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