MCQ Questions

Question No. 1

The angle of depression from the top of a cliff (CF) to a swimmer (S) is 64°. The swimmer is 55 m from the base of the cliff. Calculate the height of the cliff, correct to the nearest metre.

Answer :

Question No. 2

Two hikers, X and Y, are walking directly towards a vertical tower TW from opposite directions. Hiker X is 200 m from the tower and the angle of elevation from her position to the top of the tower is 32.6°. The angle of elevation from Hiker Y’s position to the top of the tower is 43.5°.

Answer :

a) Calculate the height of the tower, correct to two decimal places.

b) Calculate the distance between the two hikers, correct to the nearest metre.

Question No. 3

Points A, B and C are in the same vertical plane. The angle of elevation from A to C is 50° and the angle of depression from C to B is 68°. The distance from B to C is 53 cm. Calculate the distance between A and B, correct to the nearest millimetre.

Answer :

Question No. 4

A girl is standing at point G watching two kites at points K and T in the same vertical plane. The angles of elevation of the girl to the kites are α and β respectively. The distances TK : GT : GK are in the ratio 2 : 3 : 4.

Answer :

a) Express ∠TGK in terms of α and β.

b) Use the cosine rule to prove that cos(β − α) = 7/8.

c) If the angle of elevation to the nearer kite is 70°, calculate the elevation to the other kite, correct to the nearest degree.

Question No. 5

Write down the letters of the cardinal point that is directly opposite.

Answer :

a) N → ___

b) SE → ___

c) WSW → ___

d) NNE → ___

e) NE → ___

f) ESE → ___

Question No. 6

Write down the letters of the cardinal point that is halfway between the given points.

Answer :

a) N and E → ___

b) NE and SE → ___

c) NW and N → ___

d) SW and NW → ___

e) SSW and WSW → ___

f) NE and S → ___

Question No. 7

Write each of the following bearings in three-digit notation and in cardinal notation.

Answer :

a)

b)

Question No. 8

The bearing of Q from P is 045°.

Answer :

a) Write the bearing of Q from P in cardinal notation.

b) Sketch a diagram and then calculate the bearing of P from Q. Write your answer in: (i) three-digit notation; (ii) cardinal notation

Question No. 9

The bearing of D from C is S28°W.

Answer :

a) Write the bearing of D from C in three-digit notation.

b) Sketch a diagram and then calculate the bearing of C from D. Write your answer in: (i) three-digit notation; (ii) cardinal notation

Question No. 10

Three cellphone towers, K, L and M, are shown in the diagram. The bearing from L to North is 015° and from L to M is 096°. The straight-line distance between L and M is 122 km, between L and K is 270 km and between K and M is 283 km. Calculate the following bearings and write your answers in cardinal notation.

Answer :

a) L from K

b) L from M

c) K from M

Question No. 11

A tourist visits three towns, A, B and C. The straight-line distances from A to B and from A to C are 62 km and 73 km respectively. The bearings from A to B and from A to C are N 49° W and S 55° W respectively.

Answer :

a) Sketch a diagram of the triangle formed by these three towns. Show all the given information.

b) Calculate the bearing from B to A in three-digit notation.

c) Calculate the bearing from C to A in three-digit notation.

d) Calculate the size of ∠BAC.

e) Calculate the straight-line distance from B to C.

Question No. 12

A triangular field is marked off by three beacons, P, Q and R, as shown in the diagram. R is due East of P and the bearing of Q from P is N 29° E. PR = 520 m and PQ = 350 m.

Answer :

a) How far apart are beacons Q and R?

b) If a land surveyor stands on the midpoint of PR, how far is she from beacon Q?

Question No. 13

On the map, Lagos, Owerri and Yola form the vertices of an obtuse-angled triangle. Owerri is on a bearing of S 73.9° E from Lagos and Yola is on a bearing of N 73.7° E from Lagos. The straight-line distance from Lagos to Owerri is 412 km and from Lagos to Yola is 1 045 km.

Answer :

a) Sketch a diagram of this triangle using letters L, O and Y for the vertices and showing the North line at Lagos. Show all given information.

b) Calculate the size of ∠YLO.

c) Hence calculate the straight-line distance from Owerri to Yola, correct to the nearest kilometre.

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