The angles of elevation of the top of a tower from two points on the ground at distances 32 m and 18...........

Quantitative Aptitude (CPO) Height and Distance

The angles of elevation of the top of a tower from two points on the ground at distances 32 m and 18 m from its base and in the

same straight line with it are complementary. The height(in m) of the tower is .....

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SSC CPO 9th Dec 2019 Shift-2

- We have a tower and two points on the ground.

- The distances from the points to the tower are 32 m and 18 m.

- The angles of elevation from these points to the top of the tower are complementary, meaning they add up to 90 degrees.

- Let the angles be \( \theta \) and \( 90^\circ - \theta \).

- The height of the tower can be determined using trigonometry:

- From 32 m, the height \( h = 32 \cdot \tan(\theta) \).

- From 18 m, the height \( h = 18 \cdot \tan(90^\circ - \theta) = 18 \cdot \cot(\theta) \).

- Equating both expressions: \( 32 \cdot \tan(\theta) = 18 \cdot \cot(\theta) \).

- Solving the equation gives height \( h = 24 \).

Option 1: 24

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