SarkariPYQ

SSC CGL 2025 PYQ — Question 61

SSC CGL - 15 Sep 2025 - Shift 2 • Quantitative Aptitude • Q61

Back to paper

A vertical pole of height H stands on the ground. From a point P on the ground, the angle of elevationof the top of the pole is 60°. From a different point Q, located 10 meters away from point P (directly along the line extending from the base of the pole), the angle of elevation to the top of the pole is 30°. What is the height of the pole?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 53\sqrt{3}  m.

Let distance BP = x, then distance BQ = x + 10

At P:

⇒ tan60° = HxH\over x

⇒ √3 = HxH\over x

⇒ H = x√3................1

At Q:

⇒ tan30° = H(x+10)H \over (x + 10)

⇒ 1√3=H(x+10){1\over√3} = {H \over (x + 10)}

⇒ H = (x+10)√3(x + 10)\over√3...............2

Compare eq 1 and 2 

⇒ x√3 = (x+10)√3(x + 10)\over√3

⇒ 3x = x + 10

⇒ 2x = 10

⇒ x = 5

Now height:

⇒ H = x√3 = 5√3 m