Triangle DEF is an isosceles triangle with DE = FE. If DE = 5 and �ÚD = 75 degrees:

Question

what is the length of FE, the measure of angle F, and the measure of angle E?
E
D ∆ F

Answer 1

You could drop a perpendicular DP, where P is on EF, bisecting angle D and creating a right angled-triangle.
then sin37.5° = EP/5
then EF = 2EP = 2(5sin37.5°) = appr 6.0876

angle E = 90-37.5 = 52.5°

or

you could use the cosine law
EP^2 = 5^2+5^2-2(5)(5)cos75° = 37.059..
EP = √37.059... = appr. 6.0876

then use the Sine Law to find angle E