How do you find the missing side of an acute triangle when given one sides measurement and two angles?

Question

i have an acute triangle with vertices labelled D (top) E (bottom left) and F (bottom right). Angle f= 57* and angle d = 82*. The side measurement given is D->F which is 7.5m. i have to find the side E-F. Please help.

Answer 1

If you are given two angles from a triangle, then you can easily find the third angle because you know that the angles add up to 180 degrees

In this case, angle E = 180 - (82 + 57) = 41 degrees.

Now we can find the side D using the law of sines.

sin 41 / (7.5) = sin 82 / EF

EF = 7.5 * sin 82/sin 41 = 11.3