Question

Triangle ABC is split into two triangles as shown: shaded and non-shaded.

If the area of the shaded triangle is twice the area of the non-shaded triangle, find the size of angle ACB, correct to 1 decimal place.

Answer 1

26.6°

Explanation:

The area of a triangle is given by (1/2) * (base) * (height). The two triangles share the same height, so in order for the shaded triangle to have twice the area, its base must be twice that of the non-shaded triangle.

The non-shaded triangle is a right triangle with two 45° angles, so it's an isoceles right triangle with a base equal to its height.

This means that the height of the shaded triangle is 1/2 of its base. Knowing that we can get the angle of ACB with:

tan⁻¹(1/2) ≈ 0.4636476 (in radians)

Convert to decimal angle:

0.4636476 * (180/π) ≈ 26.6°