The length of the hypotenuse of a right-angled triangle is 10 cm. Find the area of the triangle

The length of the hypotenuse of a right-angled triangle is 10 cm. Find the area of the triangle if one of its corners is 30 degrees.

The ratio of the adjacent leg to the hypotenuse is equal to the cosine of the angle, therefore, the leg adjacent to an angle of 30 ° is equal to:

a = 10 * cos 30 ° = 10 * √3 / 2 = 5√3 cm.

The area of a triangle can be defined as half the product of the lengths of two adjacent sides by the sine of the angle between them:

S = 0.5 * 10 * 5√3 * sin 30 ° = 0.5 * 10 * 5√3 * 0.5 = 25√3 / 2 ≈ 21.65 cm2.