Find the area of a right-angled triangle with a hypotenuse of 8 and an angle of 15∘.

c = 8.

∠α = 15 “.

S -?

1. The area of a right-angled triangle S is determined by the formula: S = a * b / 2, where a, b are the legs of a right-angled triangle.

2. According to the definition, sinα = a / с, cosα = b / с.

3. Let us express the legs of a right-angled triangle.

a = c * sinα, b = c * cosα.

4. The area of the triangle will be determined by the formula: S = c * sinα * c * cosα / 2 = c ^ 2 * sin2 * α / 4.

S = (8) ^ 2 * sin2 * 15 “/ 4 = 64 * 0.5 / 4 = 8 cm ^ 2.

Answer: the area of a right-angled triangle is S = 8 cm ^ 2.