Chapter 8.1, Problem 62AYU

Finding the Length of a Mountain Trail A straight trail with an inclination of ${17}^{\circ }$ leads from a hotel at an elevation of 9000 feet to a mountain lake at an elevation of 11,200 feet. What is the length of the trail?

To determine

To find: The length of the trail.

Answer to Problem 62AYU

$7524.67\text{ ft}$.

Explanation of Solution

Given:

A straight trail with an inclination of $17°$ leads from a hotel at an elevation of 9000 feet to a mountain lake at an elevation of 11,200 feet.

Formula used:

$\sin \theta =\frac{\text{opposite side}}{\text{hypotenuse}}$

Calculation:

Change of elevation $=11,200-9000=2200\text{ ft}$.

Let $x$ be the length of the trail.

$\sin 17=\frac{2200}{x}$

$x=2200/\sin 17°$

$x~7524.67\text{ ft}$

The length of the trail is $7524.67\text{ ft}$.