Two straight roads diverge at an angle of 50°. Two cars leave the intersection at 2:00 P.M., one traveling at 36 mi/h and the other at 38 mi/h. How far apart are the cars at 2:30 P.M.?

Question

Two straight roads diverge at an angle of 50°. Two cars leave the intersection at 2:00 P.M., one traveling at 36 mi/h and the other at 38 mi/h. How far apart are the cars at 2:30 P.M.? (Round your answer to two decimal places.) 

Answer 1

use the law of cosines here

the triangle has angle C = 50 degrees, side a = 19, side b = 18

(angles are Capital letters, sides are lower case, side c is opposite angle C)

c² = a² + b² - (2)(a)(b)(cosC)

plug in the values to find c², then take the square root for the answer