Two observers stand 100 meters apart and observe the top of a tower. The angles of elevation are 30° and 45°. Find the height of the tower (assuming both observers are on the same side of the tower).
Show answer & explanation
Correct answer: C
Explanation
Distance of the nearer observer from the tower = x meters
Distance of the other observer = x + 100 meters
tan45° = h/x
1 = h/x
h = x
For the other observer -
tan30° = h/(x + 100)
1/√3 = h/(x + 100)
x + 100 = h√3
h + 100 = h√3
100 = h(√3 − 1)
h = 100/(√3 − 1)
h = 100(√3 + 1)/2
h = 50(√3 + 1)