From the top of a lighthouse, 100 m high, the angle of depression of a boat is ^ -1 ((5)/(12)).What is the distance between the boat and the lighthouse?

Correct answer: C. 240 m Given, angle of depression, θ= ^ -1 ((5)/(12)) aligned & θ=(5)/(12) and (100)/(x)=(5)/(12) and x=(100 × 12)/(5)=240 m aligned

NDA 2017

Exam: NDA
Year: 2017
Subject: Mathematics
Chapter: Heights and Distances

NDA 2017 · Mathematics · Heights and Distances

From the top of a lighthouse, 100 m high, the angle of depression...

From the top of a lighthouse, 100 m high, the angle of depression of a boat is \tan ^{-1} \left(\frac{5}{12}\right).What is the distance between the boat and the lighthouse?

Options

A120 m
B180 m
C240 m
D360 m

Correct answer

C. 240 m

Step-by-step solution

Given, angle of depression,

\theta=\tan ^{-1} \left(\frac{5}{12}\right) <br/>

\begin{aligned}& \Rightarrow \tan \theta=\frac{5}{12}\\ \text{\text{ and } } \Rightarrow \frac{100}{x}=\frac{5}{12}\\ \text{ and } \Rightarrow x=\frac{100 \times 12}{5}=240 \mathrm{ m}\end{aligned}

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