In DEF, given the lengths of the sides, find the measure of the stated angle to the nearest degree.

d = 10.7, e = 15.5, f = 16.2;

E=15.5 is going to be right

Using the Law of Cosines

cos (D) = (e² + f² - d²) : (2ef)

cos (D) = (240.25 + 262.44 - 114.19) / (2*15.5*16.2)

cos (D) = 388.50 / 502.20

cos (D) = 0.7735961768

D = 39.322 degrees

For the next angle we can use the Law of Sines

sin ∠E = (e • sin (D)) : d

sin ∠E = (15.5 * 0.63368) / 10.7

sin ∠E = 0.9179476636

E = 66.628 Degrees

Angle F = 180 - 39.322 - 66.628 = 74.05 degrees