Question

What is the length of EF¯¯¯¯¯? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth. ft A horizontally-aligned scalene triangle D E F. Side D E is labeled as 6 feet. Side D F is labeled as 11 feet. Angle D is labeled as 40 degrees.

Answer 1

7.5 ft

Proof in pic:

Answer 2

When finding the third side of a scalene triangle, use Law of Cosine with its formula

c^2 = A^2+B^2 - 2AB(cosC)

Now, you just have to input all your data in the formula,

c^2 = 6^2+11^2 - 2(6)(11)(cos40degrees)
c^2 = 36+121 - 2(6)(11)(cos40degrees)
c^2 = 36+121 - 2(6)(11)(0.77)
c^2 = 157 - 101.12
c^2 = 55.88
c = square root of 55.88
c = 7.48 ft

Length of EF is 7.48 ft