The height of the triangle is 5 centimeters and the angles adjacent to the base are 60 degrees

The height of the triangle is 5 centimeters and the angles adjacent to the base are 60 degrees and 45 degrees. Find the area of the triangle.

Given a triangle ABC with base AC and height BH;

BAC angle = 60 °, BCA angle = 45 °; BH = 5 cm;

In a right-angled triangle BHC, the angle HBC = 180 – 90 – 45 = 45 °, which means it is an isosceles triangle in which HC = BH = 5 cm;

In a right-angled triangle ABH, the leg ratio is BH / AH = tan (60 °) = √3, hence AH = 5 / √3;

Base AC = AH + HC = 5 / √3 + 5;

The area of the triangle is AC * BH / 2 = (5 / √3 + 5) * 5/2 = 12.5 * (1 / √3 + 1) ≈ 19.717 cm2.