DP IB Maths: AA SL

Topic Questions

3.3 Trigonometry

1a
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4 marks

Owen, Henry and Tom are rugby players passing a ball in a park. Owen is at point straight O, Henry is at point straight H and Tom is at point straight T. The distance between Owen and Henry is 25 m and the distance between Henry and Tom is 18 m. The angle straight O straight H with hat on top straight T is 96 degree.

(i)
Draw and label a diagram to represent the situation described above.

(ii)
Find the length of the line OT.
1b
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3 marks

Find the size of the angle straight O straight T with hat on top straight H.

1c
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3 marks

Find the area of the section of the park the players are using to pass the ball.

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2a
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3 marks

straight A sailboat race takes place annually for under 18’s on a large lake. The competitors must sail around five flagged buoys at the points straight A comma space straight B comma space straight C comma space straight D and straight E, in a clockwise direction.

straight B is due east of straight A comma space straight C is due south of straight B and straight A is due north of straight E
The bearing from straight A to straight C is 110° and the bearing from straight C to straight D is 220°.
The distance AB = 1200 m, the distance BC = 600 m, the distance CD = 800 m and the distances DE = EA = 1000 m.

Draw and label a diagram to show the buoys A, B, C, D and E and clearly mark the bearings and distances given above.

2b
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2 marks

The boats all start at A and must complete the course 5 times. A support motorboat is present and can travel across the course from A to C and A to D in case of an emergency.

Calculate the distance from A to C.

2c
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3 marks

Calculate the distance from A to D.

2d
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4 marks

Calculate the bearing the support boat must follow to travel from A to D.

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3a
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2 marks

The following diagram shows triangle ABC. AC = 21 km, CB = 15 km, straight A straight C with hat on top straight B = 75°.

q3-3-3-medium-trigonometry-ib-maths-

Find the area of triangle ABC.

3b
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3 marks

Find AB.

3c
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2 marks

Given that it is acute, find straight C straight A with hat on top straight B.

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4a
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1 mark

Triangle ABC has an area of 122 cm2, AB = 24 cm and BC = 11 cm.

Draw and label a diagram to show triangle ABC and clearly mark the distances given.

4b
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4 marks

Given that straight A straight B with hat on top straight C is acute, find

(i)
straight A straight B with hat on top straight C

(ii)
AC.

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5a
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3 marks

The quadrilateral ABCD shown below represents a farm paddock, where AB = 246 m, BC = 312 m and AD = 257 m. Angle straight D straight A with hat on top straight B=96° and angle straight B straight C with hat on top straight D = 78°.

q5-3-3-medium-trigonometry-ib-maths-

A fence is built connecting points B and D to split the paddock into two.

Find the length of the fence.

5b
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5 marks

Find the area of the paddock ABCD.

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6a
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2 marks

A 38 m high cliff is perpendicular to the sea and the angle of depression from the cliff to a boat at sea is 24°. Climbing the cliff is a rock climber and the angle of elevation from the boat to the climber 14°.

Draw and label a diagram to show the top of the cliff, T, the foot of the cliff, F, the climber, C, the boat, B, labelling all the angles and distances given above.

6b
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2 marks

Find the distance from the boat to the foot of the cliff.

6c
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4 marks

Find how far the climber must climb to reach the top of the cliff.

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7a
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2 marks

The diagram below shows triangle XYZ with side length YZ = 5.4 cm. The point W is placed such that XW = 5.6 cm and WZ = 4.2 cm and YW = 5.8 cm.

q7-3-3-medium-trigonometry-ib-maths-

Find the angle straight Y straight Z with hat on top straight W.

7b
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2 marks

Find the area of triangle XYZ.

7c
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3 marks

Find the area of triangle XYW.

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8a
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2 marks

The distance between towns X and Y is 134.2 km. The bearing of town X from town Y is 119°. Town Z is 54 km south of town X. The bearing of town Z from town X is 207°.

Draw and label a diagram to show towns X,Y and Z, clearly marking the bearings and distances given above.

8b
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2 marks

Calculate the distance between towns X and Z.

8c
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4 marks

Calculate the distance between towns Y and Z.

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9
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8 marks

The diagram below shows four Islands P,Q,R and S. PQ = 8.5 km, QR = 16.2 km and RS = 12.5 km. Angle straight P straight Q with hat on top straight S=25°, angle straight Q straight S with hat on top straight P = 14.7° and angle straight Q straight R with hat on top straight S = 82.1°. Island Q is due north from Island P.

q9-3-3-medium-trigonometry-ib-maths-

Mark is making deliveries around the Islands. He takes milk from Island Q to Island S, then takes wood from Island S to Island P, finally he delivers fruit from Island P to Island R.

Find the total distance Mark travels.

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10a
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2 marks

Nathan (N)  stands 10 m above the ground on the second-floor balcony of an apartment building and can see Melissa (M) in the car park. The angle of elevation from Melissa to Nathan is 21.6°.

Calculate the distance from M to N.

10b
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3 marks

Louisa (L) is standing on the other side of the car park. The distance between Louisa and Nathan is 1.5 times the distance between Melissa and Nathan.

Calculate the angle of depression from N to L.

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