Final answer:
To find the length of segment F to the nearest tenth of an inch in triangle DEF, we can use the Law of Cosines.
Step-by-step explanation:
To find the length of segment F to the nearest tenth of an inch in triangle DEF, we can use the Law of Cosines. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice their product multiplied by the cosine of the angle between them. In this case, we have:
f^2 = d^2 + e^2 - 2de * cos(F)
f^2 = 5.2^2 + 6.8^2 - 2(5.2)(6.8) * cos(166°)
f^2 = 27.04 + 46.24 - 2(35.36) * (-0.9397)
f^2 = 73.28 + 66.592(0.9397)
f^2 = 73.28 + 62.4938
f^2 = 135.7738
f ≈ √135.7738
f ≈ 11.64 inches