A ladder leaning against a wall makes an angle θ with the horizontal ground such that tan θ = \(\frac{15}{8}\). If the height of the top of the ladder from the wall is 30 m, find the distance (in m) of the foot of the ladder from the wall.

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Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 05 Jun, 2025 Shift 1)

Answer 1

Given:

tan \(\theta = \frac{15}{8}\)

Height of ladder from ground (opposite side) = 30 m

Formula used:

tan \(\theta = \frac{\text{Height}}{\text{Base}}\)

\(\Rightarrow \text{Base} = \frac{\text{Height}}{\tan \theta}\)

Calculation:

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tan \(\theta = \frac{\text{Height}}{\text{Base}}\)

\(\frac{15}{8}\) \( = \frac{\text{30}}{\text{Base}}\)

⇒ Base = \(\frac{30}{\frac{15}{8}} = 2 × 8 = 16\) m

∴ The correct answer is 16 meters.

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