A man standing on the ground observes the top of a vertical tower at an angle of elevation of 30°. He then walks 20 meters closer to the tower and observes the angle of elevation to be 60°. Find the height of the tower (in meters).

Question

Accepted Answer

Step 1: Let height of tower = h meters. Initial distance from tower = x meters.

Step 2: From first observation: tan(30°) = h/x → 1/√3 = h/x → x = h√3

Step 3: After walking 20 m closer, distance = (x - 20) meters. From second observation: tan(60°) = h/(x - 20) → √3 = h/(x - 20) → x - 20 = h/√3

Step 4: Substitute x = h√3 into the second equation:
h√3 - 20 = h/√3

Step 5: Multiply throughout by √3:
3h - 20√3 = h
2h = 20√3
h = 10√3 meters

Step 6: Approximate value: h = 10 × 1.732 ≈ 17.32 meters

Alternatively, exact form is 10√3 m ≈ 17.32 m (closest to 10√3 in standard form).

RRB Group D Trigonometry Questions

RRB Group D Trigonometry — Past Exam Questions

Study by Subtopic — Trigonometry

Study Next — Quantitative Aptitude Topics