Question

Find the area and missing angle x

Answer 1

This is an isosceles triangle, meaning that two sides and angles are the same.

x + x + 28 = 180

2x = 152

x = 76

76 degrees

using the Pythagorean Theorem, 4^2 + h^2 = 9^2

h = sqrt(65), area is 8*sqrt(65)/2 = 4*sqrt(65)

we can also check using heron's formula. area = sqrt(s(s-a)(s-b)(s-c)) = sqrt(13*4*4*5).