Pre calc question

Question

Two dogs are 15 feet from each other. Dog A is 20 feet from the favorite toy in the house. Dog b is an unknown distance from the toy, but the angle made from the toy to each dog is 34°. What is the distance(s) from the toy

to dog b.

Answer 1

let x = the distance from toy to dog B

by law of cosines

15^2 = 20^2 + x^2 - 2(x)(20)cos34

225 = 400 + x^2 -40x(.829)

x^2 -33.16x - 175 = 0

x = 33.16/2 + or - (1/2)sqr(33.16^2 +4(175)) = 37.79 feet from toy to B

x = 37.79 feet rounded off to 2 decimal places.

Answer 2

Law of Cosines

15² = 20² + d² - 2(20)(d) cos 34°