Part 1) We need to use the Law of Cosines to find the missing side.
Part 2) Let's label the missing side as c. According to the Law of Cosines:
c^2 = a^2 + b^2 - 2ab cos(C)
Where a and b are the known sides adjacent to the missing side, and C is the angle opposite to the missing side. In this case, a = 30 ft, b = 50 ft, and C = 25 degrees. Substituting these values:
c^2 = 30^2 + 50^2 - 2(30)(50)cos(25)
c^2 = 1062.44
Taking the square root of both sides:
c ≈ 32.6 ft
Therefore, the third side of the garden is approximately 32.6 ft long.
A landscaper is building a triangular garden behind a house. The lot is bounded on one side by the house that is 30 ft. long and on another side by a fence that is 50 ft. long. If the fence makes a 25 degree angle with the house, how long is the 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
Part 2) Show all work to find the missing side. Make sure to put what equation you are using and the work to solve it.
1 answer
1 answer