ECZ 2016 · O-Level Paper 2 · Question 10 — Trigonometry
The diagram shows the location of three secondary schools, namely Kamubala (K), Belengani (B) and Pendeni (P) in a district. P is 5 km from K, B is 3 km from K and angle PKB = 110 degrees.
(a(i)) The diagram shows three secondary schools Kamubala (K), Belengani (B) and Pendeni (P). P is 5 km from K, B is 3 km from K and angle PKB = 110 degrees. Calculate BP.[5]
Verified working — step 1
By the cosine rule:(a(ii)) Calculate the area of triangle BKP.[2]
Verified working — step 1
Area = (12)(5)(3) sin 110(a(iii)) Calculate the shortest distance from K to BP.[2]
Verified working — step 1
The shortest distance is the perpendicular height h from K to BP.(b) Solve the equation tan(theta) = 0.7 for 0 <= theta <= 180 degrees.[1]
Verified working — step 1
theta = arctan(0.7) = …(c) Simplify 17k^220a^2divided by 51k^25a.[2]
Verified working — step 1
Multiply by the reciprocal: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.
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