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)

Question

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), 2 m, 4 m, 6 m, 8 m

MARKS App · Accepted Answer

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

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