Question

A man travels at 42 degrees northwest, and ends up 8.5 miles west of his starting point. How far did he travel?

Answer 1

Answer:

The man traveled 12.70 miles.

Step-by-step explanation:

We can find the distance traveled by the man knowing:

$d_{W}$: the distance at the west = 8.5 miles

$\theta_{NW}$: the northwest angle = 42°

Then by using the following trigonometric identity we have:

$sin(\theta) = \frac{d_{W}}{d_{NW}}$

$d_{NW} = \frac{d_{W}}{sin(\theta)} = \frac{8.5 miles}{sin(42)} = 12.70 miles$

Therefore, the man traveled 12.70 miles.

I hope it helps you!