Question

Three points on the ground form a right triangle  ABC with right angle at B . The distance BC m =120 . A vertical tower of height H stands at A . The elevation angle of the tower top is 60° from B and 45° from C . Find H

Answer 1

Given : Three points on the ground form a right triangle   ABC with right angle at B . BC = 120 m. A vertical tower of height H stands at A . The elevation angle of the tower top is 60° from B and 45° from C

To find : Height of Tower

Solution:

BC = 120 m

Let say  height of Tower  = H  m

Tower is at A

elevation angle of the tower top   60° from B

=> Tan 60 ° = Tower Height / AB

=> √3  = H / AB

=> AB = H/√3

AC² = AB²  + BC²

=> AC² = (H/√3)² + 120²

=> AC² = H²/3 +  120²

=> AC²  = ( H² + 3 * 120²)/3

elevation angle of the tower top   45° from C

=>  Tan 45 ° = Tower Height / AC

=> 1 = H/AC

=> H = AC

=> H² = AC²

=> H² = ( H² + 3 * 120²)/3

=> 3H² = H² + 3 * 120²

=> 2H² = 3 * 120²

=> H = 120 √3 / √2

Height of Tower = 120 √3 / √2

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