Question

Your team is located at a point 58 feet east of the building. The team leader gets the best signal if he travels 34 feet from camp at a 102 degree angle. How far will your team leader be from the building when he is done travelling?

Answer 1

`74.4` feet.

Explanation:

The path defines a triangle with sides 58 and 34 with an internal angle of `105^o`. We can use the Law of Cosines to find the unknown side, which is the distance from the building to the new point.
`a^2 = b^2 + c^2 -(2bc)cosA`; `a^2 = 58^2 + 34^2 -2xx58xx34cos105`
`a^2 = 4520 + 1021`; `a = 74.4` feet.