In a right-angled triangle ABC, the angle C = 90, and the outer angle at the vertex B = 120

In a right-angled triangle ABC, the angle C = 90, and the outer angle at the vertex B = 120 *. Find the length of the leg BC if the hypotenuse AB = 8

1) Find the inner angle at the vertex B in the triangle ABC:

The sum of the outer angle at the vertex B and the inner angle B is equal to 180 ° (adjacent angles), the angle B is equal to:

B = 180 ° – 120 °;

B = 60 °.

2) Find the length of the leg BC, knowing the hypotenuse AB and angle B.

The cosine of angle B is equal to the ratio of the adjacent leg BC to the hypotenuse AB:

Cos B = BC: AB.

BC = AB × cos B,

According to the condition AB = 8 cm, and cos B = cos 60 ° = 1/2, substitute the values into the equation and solve it:

BC = 8 × 1/2;

BC = 8: 2;

BC = 4 cm.