An observer finds that the angular elevation of a tower is θ . On advancing 3 m towards the tower, the elevation is 45 o and on advancing 2 m further more towards the tower, the elevation is 90 o - θ . The height of the tower is (assume the height of observer is negligible and observer lies on the same level as the foot of the tower)

Step-by-step solution

Let, P Q be the tower of height h meters ∠ P A Q = θ , ∠ P B Q = 45 o and ∠ P C Q = 90 o - θ A B = 3 m and B C = 2 m ⇒ 3 = A B = P A - P B = h cot ⁡ A - h and 2 = B C = P B - C P = h - h tan ⁡ A ∴ h + 3 h = cot ⁡ A , h - 2 h = tan ⁡ A ∴ h + 3 h · h - 2 h = 1 ⇒ h 2 + h - 6 = h 2 ⇒ h = 6 m