Law of cos trigonometry

Question

wo hikers, Sonia and Tony, leave the same point at the same time. Sonia walks due east

at the rate of 3 miles per hour, and Tony walks 45◦ north of east at the rate of 4.3 miles

per hour. How far apart are the hikers after 3 hours? Round to one decimal place.

2

Answer 1

Sonia walks east for a distance of 3 mph * 3 hours (9 mi.)

Tony walks northeast at 4.3 mph * 3 hours (12.9 mi.)

x² = 12.9² + 9² - 2(12.9)(9)cos45º

x² = 247.41 – (232.2)(√2/2)

x² = 247.41 – 164.19

x² = 83.22

x = 9.1 mi.