The angle of elevation of the top of a vertical tower from a point A, due east of it is 45 o . The angle of elevation of the top of the same tower from a point B, due south of A is 30 o . If the distance between A and B is 54 2 m , then the height of the tower (in meters), is:

Step-by-step solution

Let height of the tower be 'H' Let A P = x B P = y In ∆ A P Q ⇒ tan ⁡ 45 o = H x   ⇒     H = x In ∆ B P Q ⇒ tan ⁡ 30 o = H y     ⇒     y =   3   H Since, ∆ A P B is a right-angled triangle. ⇒ x 2 + 54 2 2 = y 2 ( Pythagoras Theorem ) ⇒ H 2 + 54 2 2 = 3 H 2 ⇒ 54 2 2 = 2 H 2 ⇒ 54 2 =   2 H ⇒ 54 = H