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A vertical tower CP subtends the equal angle $θ$ at point $B$ on the horizontal plane through C , the foot of the tower and at point A in the vertical plane. If the triangle ABC is equilateral with length of each side equal to 4m, the height of the tower is__________

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answer is 2.

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Detailed Solution

Clearly

∠ C B P = C A P = θ

(angle in same segment) and PCBA is a cyclic quadrilateral.

⇒ B A P + B C P = 1800 ⇒ B A P = 900 C = B C P ¯ = 900 ⇒ P B C = θ = B A P − B A C = 900 − 600 = 300

If H be the height of the tower, then CP

⇒ H = 433 m = 2.31

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