MCQ Questions

Question No. 1

Each of the triangles on the next page has an indicated angle. The sides are marked with their lengths, given as numbers or variables (letters). For each triangle, state which side is the hypotenuse, opposite or adjacent to the designated angle. Record the lengths and variable letters in the table below

Answer :

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Question No. 2

Draw an angle of 75°.

Answer :

Question No. 3

Create any three right-angled triangles, just like you did in the section above.

Answer :

Question No. 4

Fill in the table and compute the ratios.

Answer :

Question No. 5

Complete each of the following using △ABC.

Answer :

a) sin A

b) cos A

c) tan A

d) sin C

e) cos C

f) tan C

Question No. 6

For the given triangle, tan θ = 12/9.

Answer :

a) Fill the 12 and 9 in the correct position on the diagram.

b) Find the remaining side.

c) Determine sin θ.

Question No. 7

Fill in the missing angle.

Answer :

a) tan… = 20/15

b) sin… = 15/25

c) cos… = 15/25

Question No. 8

Copy and complete this table, using a scientific calculator. All results should be given to four decimal places.

Answer :

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Question No. 9

Use tables to determine the following.

Answer :

a) tan 65°

b) sin 38°

c) cos 74°

d) tan 49°

e) cos² 26°

f) ¼ cos 20°

Question No. 10

Use a calculator to determine the following.

Answer :

a) tan 45°

b) 3 sin 27.3° − 2

c) (sin 16.1°) ⁄ (cos 73.9°) − 2 sin 30°

Question No. 11

If A = 60° and B = 35°, determine the following to two decimal places.

Answer :

a) sin (A + B)

b) sin A + sin B

c) cos² A

d) 2 cos A

e) tan (A⁄B)

f) 1 ⁄ cos A − 1 ⁄ sin B

Question No. 12

Use your calculator to find the following. Give your answers correct to one decimal place.

Answer :

a) the acute angle with sine of 0.62

b) the acute angle with cosine of 0.434

c) the acute angle with tangent of 4.83

d) the acute angle with sine of 6/17

e) cos⁻¹(2/3)

f) tan⁻¹(1/8).

Question No. 13

Use tables or a calculator to determine the following angles, correct to one decimal place.

Answer :

e) sin θ = 2/3

a) tan θ = 1.7

b) sin θ = 0.8

c) cos θ = 0.32

d) tan θ = 5 3/4

f) cos α = 1.2

g) 4 cos θ = 3

h) cos 4 θ = 0.3

i) sin α + 2 = 2.65

Question No. 14

Find the size of the unknown angle in each diagram. Give your answer correct to the nearest degree.

Answer :

a)

b)

c)

d)

e)

f)

Question No. 15

Find the unknown sides in the figures below. Give your answers to the same number of decimal places as given in each side length on the figure.

Answer :

a)

b)

c)

d)

e)

f)

Question No. 16

If cos θ = 4/5, find the value of:

Answer :

a) sin θ

b) tan θ

Question No. 17

If sin θ = 12/13, find the value of:

Answer :

a) 2 cos θ + 3 sin θ

b) tan³ θ

Question No. 18

Solve for x and y in the following triangles. Use trigonometry only.

Answer :

a)

b)

Question No. 19

Use the figure to find:

Answer :

a) the length of AC

b) the length of BC

c) the length of AB.

Question No. 20

Find the sides labelled x and y in the figure below.

Answer :

Question No. 21

Use the lengths shown in the figure to calculate:

Answer :

a) (sin 30°)² + (cos 30°)²

b) (sin 60°)² + (cos 60°)²

Question No. 22

Use the diagram and determine:

Answer :

a) CD

b) AB

Question No. 23

In a right-angled triangle, one angle is 50°. The side opposite this angle is 5 cm. What is the length of the hypotenuse side?

Answer :

Question No. 24

In a right-angled triangle, the hypotenuse is 8 m and one angle is 55°. What is the length of the shortest side?

Answer :

Question No. 25

Hassana is standing beside a lighthouse on a sunny day. She measures the length of her shadow, which is 4.8 m and the length of the shadow cast by the lighthouse, which is 75 m. Hassana is 1.6 m tall. How tall is the lighthouse? (Draw a diagram to help solve the problem.)

Answer :

Question No. 26

Ibekwe flies a kite on a 17 m string at an inclination of 63°.

Answer :

a) What is the height h of the kite above the ground?

b) If Ibekwe’s friend Egbede stands directly below the kite, calculate the distance between the two friends.

Question No. 27

The length of a rope, from the top of a mast to a point 20 m from the foot of a mast, is 60 m. Calculate the height of the mast.

Answer :

Question No. 28

A boy travels in a boat at an angle of 20° to the river bank. If he travels 200 m before reaching the opposite bank, calculate the width of the river.

Answer :

Question No. 29

Determine the length of the diagonal across the floor of a hall, if the width of the hall is 20 m and the angle the diagonal makes with the width is 70°. Calculate the length of the hall.

Answer :

Question No. 30

When a ladder of length 25 m rests against a wall, it makes an angle 37° to the wall. Find the distance between the wall and the base of the ladder.

Answer :

Question No. 31

Determine:

Answer :

a) PQ

b) PR

c) P̂

Question No. 32

A rectangle has sides of length 18 cm and x cm. The acute angle between the diagonals of the rectangle is 40°. Determine x.

Answer :

Question No. 33

A right-angled triangle has sides of lengths 5 m, 12 m and 13 m. Calculate, to one decimal place, the sizes of all the angles in this triangle.

Answer :

Question No. 34

Use the figure on the right to determine the values of:

Answer :

a) TU

b) SV

c) ST̂V

Question No. 35

Use the figure below to find the values of:

Answer :

a) PQ

b) PR

c) SP

Question No. 36

In the figure, AB̂C = AĈD = 90°, AĈB = 30° and AD̂C = 45°. Given that CD = 10 cm:

Answer :

a) State the length of AC

b) Calculate the length of AB.

Question No. 37

In the figure, AD = 8 cm, CD = 17 cm, BC = 5 cm and CÂD = 90°. Find:

Answer :

a) AC

b) AB

c) BD.

Question No. 38

The diagram shows a trapezium ABCD, in which AB̂C = BÂD = 90°, AB = 8 cm, BC = 16 cm and AD = 10 cm. Calculate the perimeter of the trapezium.

Answer :

Question No. 39

The lengths of the sides of an isosceles triangle are 10 cm, 10 cm and 16 cm. Find the sizes of the angles of the triangle.

Answer :

Question No. 40

In ΔPQR, the point S lies on QR, such that PS is perpendicular to QR. Given that PS = 7 cm, SR = 24 cm and QS = 5 cm, calculate:

Answer :

a) to two decimal places, the lengths of PQ and PR

b) to the nearest degree, PQ̂R, PR̂Q and QP̂R

c) the area of ΔPQR.

Question No. 41

In the figure, AB is a chord of the circle. Given that AB = 24 cm and AÔB = 120°, calculate:

Answer :

a) the exact value of the radius of the circle

b) the area of ΔAOB.

Question No. 42

Kufreabasi stands on land, 200 m away from one of the towers on a bridge. He reasons that he can calculate the height of the tower by measuring the angle to the top of the tower and the angle to its base at water level. He measures the angle of elevation to its top as 37° and the angle of depression to its base as 21°. Calculate the height of the tower to the nearest metre.

Answer :

Question No. 43

Amadia works for an oil company. She needs to drill a well to an oil deposit. The deposit lies 2 300 m below the bottom of a lake, which is 150 m deep. The well must be drilled at an angle from a site on land. The site is 1 000 m away from a point directly above the deposit. Determine the angle at which the well should be drilled.

Answer :

Question No. 44

From the top of the Chrysler Building, which is 320 m high, the angle of elevation to the top of the Empire State Building is 26°, and the buildings are 250 m apart. The angle of depression from the Chrysler Building to the foot of the Empire State Building is x. If the buildings are in the same horizontal plane, calculate:

Answer :

a) x, the angle of depression

b) the height of the Empire State Building.

Question No. 45

Tutu and Abadom are trying to determine the height of the flagpole, AB, using trigonometry. Tutu stands 20 m away from Abadom. They are on opposite sides of the pole. The angle of elevation from Tutu to the top of the pole is 29°, while the angle of elevation from Abadom to the top of the pole is 48°. Determine the height of the flagpole, AB.

Answer :

Question No. 46

Calculate the height of a cliff, if the angle of depression of a boat at sea is 42°. The boat is 700 m away from the foot of the vertical cliff.

Answer :

Question No. 47

The height of a lighthouse is 30 m. The angle of depression of a ship is 7°. Calculate the distance of the ship from the lighthouse.

Answer :

Question No. 48

Find the length of the shadow of a flagpole that is 80 m tall, when the altitude of the Sun is 25°.

Answer :

Question No. 49

A boy who is 1.6 m tall observes the angle of elevation of the top of a coconut tree to be 28°. The boy is standing 20 m from the foot of the coconut tree. Find the height of the tree.

Answer :

Question No. 50

To find the height of a tower, a girl took measurements from two points that were in a straight line on horizontal ground at the foot of the tower. The angles of elevation of the top of the tower from the two points were 19° and 27°. The points were 60 m apart.

Answer :

a) Sketch a diagram of the measurements.

b) Calculate the distance from the nearest point to the foot of the tower. Hence calculate the height of the tower.

Question No. 51

A man standing 80 m away from a tower observes the angles of elevation to the top and bottom of a flagpole standing on the tower as 41° and 37°, respectively. Calculate the height of the flagpole.

Answer :

Question No. 52

A car drives for 6 km at a bearing of 030°. How far north is the car from its starting point?

Answer :

Question No. 53

A beach is on a bearing of 064° from an airport, at a distance of 20 km. How far east is the beach from the airport?

Answer :

Question No. 54

Town B lies at a bearing of 037° from Town A, and Town C is at a bearing of 127° from Town B. The distance between Town A and Town B is 7 km, and the distance between Town B and Town C is 11 km.

Answer :

a) Determine the distance between Town A and Town C.

b) Determine the bearing of Town A to Town C.

Question No. 55

The bearing of X from P is 090° and the bearing of Y from P is 180°. Given that the distances PX and PY are 20 km and 25 km respectively, calculate:

Answer :

a) the bearing of X from Y

b) the bearing of Y from X.

Question No. 56

P is 15 km from O on a bearing of 000° and Q is 9 km from O on a bearing of 270°. A boy starts from Q and rides in the direction 020°

Answer :

a) Calculate the distance the boy has to ride before his bearing from P is 270°.

b) Find the distance he is from P when his bearing is 270° from P.

c) Find his bearing at point P from O.

Question No. 57

Three towns X, Y and Z lie on a straight road on a bearing 090° from X. Y is 10 km from X and Z is 25 km from X. Another town P is 10 km from X on a bearing 150° . Calculate:

Answer :

a) the distance and bearing of P from Y

b) the distance and bearing of P from Z.

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