ECZ 2010 · O-Level Paper 2 · Question 8 — Trigonometry

P, Q and R are fishing camps along the banks of Lake Kariba joined by straight paths PQ, QR and RP. P is 7.6 km from Q, and Q is 13.2 km from R and angle PQR = 120°.

(a) Calculate

(a(i)) the distance PR,[5]

Verified working — step 1

Two sides and the included angle: cosine rule.

(a(ii)) the area of triangle PQR.[3]

Verified working — step 1

Two sides enclose the angle at Q, so use the area rule.

(b) Find the shortest distance from Q to PR.[2]

Verified working — step 1

The shortest distance is the perpendicular height from Q to PR.

(c) A fisherman takes 30 minutes to move from R to P. Calculate his average speed in km/h.[2]

Verified working — step 1

30 minutes is 0.5 hours, and RP = 18.23 km.

The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.

Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

Have a different question?

Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.