JAMB Mathematics 1987 Question 40

Question 40

Trigonometry

From two points X and Y, 8cm apart, and in line with a pole, the angle of elevation of the top of the pole are 30 and 60 respectively. Find the height of the pole, assuming that X, Y, and the foot of the pole are on the same horizontal plane and X and Y are on the same side of the pole.

A.4m
B.3√3/3 m
C.4√3 m
D.8√3m

Show the answer and explanation

Answer: C (4√3 m)

Explanation

Let Y be a from the foot. Then h = a tan 60° = a√3 and h = (8 + a) tan 30° = (8 + a)/√3. So 3a = 8 + a, a = 4 and h = 4√3.