EXPLAIN PLEASE??

Question

A landscaper is building a triangular garden behind a house. The lot is bounded on one side by the house that 30ft. Long and on another side by a fence that is 50ft long. If the fence makes 25° angle with the house, long is third side of the garden? Round your answer to the nearest foot

part 1) which law is needed to find the missing side

a)law of sines

b)law of cosines

show work please

Answer 1

You should use the law of cosines because since you are given two sides and an angle that IS included, this is not enough information to use the law of sines (the angle would need to be non-included):

c = √(a²+b²-2ab·cosθ)

c = √(30²+50²-2(30·50·cos25°)) ≈ 26.1ft

Hence, the missing side is about 26.1 feet. Hope this helped!