Question

16. You and a friend are going shopping. You leave school and drive 10 miles

due west on 26th Street. You then drive 7 miles NW on Raspberry Street to the
grocery store. Your friend leaves school and drives 10 miles due east on 26th Street.
He then drives 7 miles SE on Cascade Street to the movie store. Each of you has
driven 17 miles. Which of you is farthest from your school?

Answer 1

My friend is farthest from my school

Explanation:

Let the distance from the movie store to school be x and the distance from the grocery store to school be y

Using Cosine rule,

x²= 10²+7² - 2×10×7Cos120

x²= 149 -140(-0.5)

x²= 149+70

x²= 219

x= √219

= 14.8miles

y²= 10²+7² - 2×10×7Cos100

y²= 149 -140(-0.1736)

y²=149+24.2704

y²=173.2704

y=√173.2704

y=13.4miles