# Bong walks 100 m due North and then 150 m in a direction N 37 deg. E. How far is Bong from his original position?

Apr 19, 2018

color(purple)("Bong is " 181.38 m " away from the original position"

#### Explanation:

Applying Law of Cosines,

${c}^{2} = {a}^{2} + {b}^{2} - 2 \cdot a \cdot b \cdot \cos C$

$\text{ Given : } b = 100 m , a = 150 m , \hat{C} = 180 - 37 = {143}^{\circ}$

c = sqrt((100^2 + 150^2 - (2 * 100 * 150 * cos 143))

$c = \sqrt{10000 + 22500 - 500 \cos 143}$

color(purple)(c = 181.38 m