Area of Triangles Problem Solving

Question

a painter needs to find the area of the gable end of a house. what is the area of the gable if it is a triangle with two sides of 42 ft that meet at a 105° angle?

round to the nearest hundredth.

Answer 1

Compute the height of the triangle by bisecting the 105 degree angle.

Height, h = 42 * (cos 52.5 degrees) = 25.6 feet

Base, b = 2 * 42 * (sin 52.5 degrees) = 2 * 33.3 = 66.6 feet

Recall the mnemonic: SOH CAH TOA.

Sin is the opposite side (in this case 1/2 of the base).

Cos is the adjacent (in this case the height).

Area of a triangle = 1/2 * b * h = 1/2 * 25.6 * 66.6 = 852.5 square feet.