Calculating Height Using Trigonometric Ratios Given Angles

Question

Given that P is the top and Q is the foot of a tower standing on a horizontal plane, and A and B are two points on this plane such that AB is 30m and QAB is a right-angle, it is found that cot∠PAQ = 2/7 and cot∠PBQ=3/7. How can I find the height of the tower?

Answer 1

Q is a point on a horizontal plane. Logically, PQ is perpendicular to the plane. A and B are points in the plane.

Therefore, ∠PQA is a right angle, and ∠PQB is a right angle.

cot ∠PAQ = 2/7 → AQ / PQ = 2/7 → AQ = (2 PQ) / 7

cot ∠PBQ = 3/7 → BQ / PQ = 3/7 → BQ = (3 PQ) / 7

(AQ)² + 30² = (BQ)²

(4/49)(PQ)² + 900 = (9/49)(PQ)²

900 = (5/29)(PQ)²

8820 = (PQ)²

93.91 = PQ

Answer 2

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