An isosceles triangle has a height of 12.5 m (measured from the unequal side) and two equal angles that measure 55°. Determine the area of the triangle.

Question

Split in half the triangle is a right triangle, so it's three angles are 90%, 55% and 70%.

I'm still not sure how to find the area.

Answer 1

If the base is 2x, then

12.5/x = tan 55°

The area is just 12.5x

Answer 2

If you split it in half, the three angles are 90, 55, and 35 for one half. You basically find the base of one half of the triangle, multiply it by 2 (to find the base of the full triangle), multiply that by the height and divide it by 2:

tan55=12.5/x
xtan55/tan55=12.5/tan55
x=8.7526 (Rounded)

2x=2(8.7526)=17.5052 (Rounded)

A=bh/2
A=(17.5052)(12.5)/2
A=109.4m^2 (Rounded)