Question

Carlos walked 10 miles at an angle of 20 degrees north of due east. To the nearest tenth of a mile, how far east, x, is Carlos from his starting point?

Answer 1

9.4 miles

Explanation:

If Carlos walked 10 miles at an angle of
`20\degree` north of due east, then how far he moved east, which is
`x` can be calculated using trigonometry.

The side opposite to the known angle is
`x` miles.

The hypotenuse of the right triangle formed is
`10` miles.

We use the cosine ratio to obtain;

`\cos(20\degree)=(x)/(10)`

`\Rightarrow x=10\cos(20\degree)`

`\Rightarrow x=9.396926208`

`\therefore x=9.4` miles to the nearest tenth.