In ΔDEF, d = 5.2 inches, e = 6.8 inches and ∠F=166°. Find the length of f, to the nearest 10th of an inch

Answer 1

Since we have two side lengths and an angle, we can use the Law of Cosines to find the length of the final side.

In this case we can write the law of cosines as: f² = d² + e² - 2(de)(cos(F))

f² = 5.2² + 6.8² - 2(5.2)(6.8)cos(166)

f² = 27.04 + 46.24 - 66.56 cos (166)

f² = 73.28 - 66.56 cos 166

f = √(73.28 - 66.56 cos 166) ≈ 11.9 ft.