From a point A on the ground, the angle of elevation to the top of a tower is 45°. From another point B, 40 meters closer to the tower along the same straight line, the angle of elevation is 60°. Find the approximate height of the tower and the distance from point A to the base of the tower.
Show answer & explanation
Correct answer: A
Explanation
Let the height of the tower = h meters and the distance from A to the base of the tower = x meters.
From A,
tan45° = h/x
h = x
B is 40 meters closer to the tower than A.
Therefore, the distance from B to the base = x − 40
tan60° = h/(x − 40)
√3 = h/(x − 40)
Since h = x,
√3 = h/(h − 40)
h = √3(h − 40)
h = 1.732h − 69.28
0.732h = 69.28
h ≈ 94.64 ≈ 95 meters