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

The man traveled 12.70 miles.

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) = (d_(W))/(d_(NW))`

`d_(NW) = (d_(W))/(sin(\theta)) = (8.5 miles)/(sin(42)) = 12.70 miles`

Therefore, the man traveled 12.70 miles.

I hope it helps you!