MCQ Questions

Question No. 1

Solve △ABC if Bˆ = 50°, Cˆ = 47° and AC = 25 units.

Answer :

Question No. 2

Solve △DEF if Dˆ = 39°, DE = 3 cm and EF = 6 cm.

Answer :

Question No. 3

Solve each of the triangles provided.

Answer :

a) b) c) d)

Question No. 4

Solve each of the following. (Hint: Sketch a diagram of each triangle and write in the given measurements.)

Answer :

a) ΔABC with Â = 105°, B̂ = 22° and AB = 19 cm

b) ΔDEF with DE = 72 m, EF = 65 m and F̂ = 58°

c) ΔJKL with Ĵ = 79°, K̂ = 57° and KL = 5.5 units

d) ΔMNO with N̂ = 124°, MN = 3 mm and MO = 8 mm

e) ΔPQR with R̂ = 37.2°, Q̂ = 34.5° and PR = 73 m

f) ΔXYZ with Ẑ = 60.4°, XY = 7 units and YZ = 5 units

Question No. 5

Find both solutions to each of the following.

Answer :

a) ΔABC with B̂ = 58°, AB = 4 cm and AC = 3.5 cm

b) ΔDEF with D̂ = 76.1°, DF = 43 mm and EF = 42 mm

c) ΔJKL with K̂ = 44°, JL = 50 units and KL = 65 units

d) ΔPQR with R̂ = 41°, PQ = 17 m and PR = 19 m

Question No. 6

In each ΔXYZ, calculate the size(s) of Ŷ.

Answer :

a) X̂ = 25°, XZ = 6.9 units and YZ = 4.8 units

b) Ẑ = 45°, XY = 5 cm and XZ = √50 cm

c) X̂ = 30°, XZ = 17.94 km and YZ = 8.97 km

d) Ẑ = 50°, XY = 64 mm and YZ = 80 mm

Question No. 7

Solve each of the triangles below.

Answer :

a)

b)

c)

d)

Question No. 8

Solve each of the following with the aid of a diagram.

Answer :

a) ΔABC with AB = 5 cm, BC = 6 cm and AC = 7 cm

b) ΔDEF with DE = 1.2 km, DF = 1.3 km and D̂ = 124°

c) ΔJKL with Ĵ = 85°, JK = 169 units and JL = 137 units

d) ΔMNO with MN = 6 mm, NO = 4 mm and MO = 9 mm

e) ΔPQR with PQ = 301 m, PR = 473 m and QR = 338 m

f) ΔXYZ with XY = 19.5 km, YZ = 14 km and Ŷ = 21.6°

Question No. 9

A boy is standing at the edge of a river at point A. His friend is standing directly opposite him, on the opposite bank of the river, at point B. A third friend is swimming in the river, at point C, such that ∠ACˆB = 49°, ∠ABC = 60° and AC = 45 m. Calculate the width of the river between points A and B.

Answer :

Question No. 10

Two straight roads lead from Town X, with an angle of 146° between them. Two vehicles leave Town X at the same time. The average speeds of the vehicles are 80 km/h and 95 km/h respectively. After one hour, the slower vehicle has reached point Y and the faster vehicle has reached point Z. Calculate the distance between points Y and Z, correct to the nearest kilometre.

Answer :

Question No. 11

Two people, M and N, leave their apartment block (A) to visit friends at the same time. They each walk along a straight road. The angle between the roads is 37°. By 20:00, person M has walked a distance of 5.2 km, and the two people are 3.25 km apart.

Answer :

a) Explain why there are two different solutions to △MNA.

b) Sketch the complete diagram of this situation, showing both possible solutions.

c) Calculate the two possible distances that person N walked. Give your answers correct to two decimal places.

Question No. 12

A parallelogram has sides of 30 mm and 90 mm. The length of the longer diagonal is 105 mm. Calculate the length of the shorter diagonal, correct to the nearest millimetre.

Answer :

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