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SSC CGL 2022 PYQ — Question 67

SSC CGL - 20 April 2022 - Shift 2 • Quantitative Aptitude • Q67

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A and B are two points on the same side of a ground, 50 metres apart. The angles of elevation of these points to the top of a tree are 60° and 30°, respectively. What is 40% of te height of te tree(in m)?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 103\sqrt{3}

Let the height of the tree be H and the distance between the foot of the tree to the point A be x

Now,

H/x = tan 60 = (3)½

⇒ H/x = (3)½x

Again,

H/(x + 50) = tan 30

⇒ H/(x + 50) = 1/(3)½

H = (x + 50)/(3)½

Now,

(3)½ = (x + 50)/(3)½

⇒ 3x = x + 50

⇒ 2x = 50

⇒ x = 25

Now,

H/25 = (3)½

⇒ H = 25(3)½

Now,

40% of the height of the tree =  25(3)½ × 40% = 10(3)½