. Michael leaves home and drives 17 miles west to work. After work, he travels 9 miles to a friend's

house. If the bearing from work to the friend's house is S 24 E, find the distance between the

friend's house and home.

The distance between friends's house and home is 15.67 miles.

Step-by-step explanation:

See the attached diagram.

We have Δ HWF whose HW = 17 miles, WF = 9 miles and ∠ HWF = (90° - 24°) = 66°.

We have to find FH.

Now, using the property of triangles we can find the length FH.

We have, FH² = HW² + WF² - 2 × HW × WF × Cos ∠ HWF

⇒ FH² = 17² + 9² - 2 × 17 × 9 × Cos 66°

⇒ FH² = 245.54

⇒ FH = 15.67 miles

Therefore, the distance between friends's house and home is 15.67 miles. (Answer)