The leg of a right-angled triangle is 8 cm, the angle adjacent to this leg is 60 degrees. Find the S of the triangle.

1. Vertices of the triangle – A, B, C. ∠C = 90 °. ∠А = 60 °. S – area.

2. We calculate the length of the hypotenuse AB through one of the trigonometric functions ∠A (cosine). Cosine ∠A is the quotient of dividing the length of the AC leg adjacent to it by the length AB.

AC: AB = cosine 60 ° = 1/2.

AB = AC: 1/2 = 8: 1/2 = 16 centimeters.

3. Calculate the length of the BC leg:

ВС = √АВ²-АС² (by the Pythagorean theorem).

BC = √16²- 8² = √256 – 64 = √192 = 8√3 centimeters.

4. S ΔABS = AC x BC / 2 = 8 x 8√3 / 2 = 32√3 centimeters².