Chapter 8.1, Problem 52AYU

Finding the Distance of a Ship from Shore A person in a small boat, offshore from a vertical cliff known to be 100 feet in height, takes a sighting of the top of the cliff. If the angle of elevation is found to be ${25}^{\circ }$, how far offshore is the boat?

To determine

To find: The distance of a ship from shore.

Answer to Problem 52AYU

$\text{214}\text{.45 feet}$.

Explanation of Solution

Given:

The cliff $\text{height }=100\text{ feet}$ and angle of elevation $={\text{ 25}}^{\circ }$ are given.

Formula used:

$\tan \theta \text{ = }\frac{\text{opposite side}}{\text{adjacent side}}$

Calculation:

In order to find we have to use $\tan$ ratio so that we can find the distance between boat and cliff base3.

$\tan {25}^{\circ }\text{ = }\frac{\text{height}}{\text{distance}}$

$\text{Distance = }\frac{\text{height}}{\tan {25}^{\circ }}$

$=\frac{100}{0.4663}$

$\approx 214.45\text{ feet}$.