How far apart are the ducks from the house?

Question

Ducks are visting a local pond. The angle ay the treeis 28°. The house is 26 feet from the tree and the tree is 47 feet from the ducks. How far apart are the ducks from the house?

Answer 1

I start by drawing a picture of the triangle DTH, with each letter representing what is at each vertex of the triangle — ducks, tree, and house respectively. We know the distances TH = 26 feet and TD = 47 feet, as well as the measure of angle T = 28°.

Since we know two sides and the included angle in the triangle, we can use the Law of Cosines to find the measure of the final side DH, the distance the ducks are from the house:

DH = √ (26² + 47² – 2 • 26 • 47 • cos 28°)

Rounded to two places, the ducks are 26.96 feet away from the house.