Michael leaves home and drives 17 miles west to work. after work he travels 9 miles to a friend’a house. if the bearing from work to the friend’s house is S 24degree E, find the distance between the friend’a house and home.

The distance between the friend's house and home is 14.263 miles.

Explanation:

Base, b = 17 miles

angle, S = 24°

Distance between friend's house and home, p = ?

We know,

tan 24° = p/b

tan 24° = p/17

0.839 = p/17

p = 14.263 miles

Therefore, distance between the friend's house and home is 14.263 miles.

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!