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
Answers
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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