In triangle ABC, angle C = 60 degrees, angle B = 90 degrees. Height BB1 = 2cm. find AB.

In triangle ABC it is known:

Angle C = 60 °;
Angle B = 90 °;
BB1 height = 2 cm.
Find AB.

1) Find the angle A of the triangle ABC.

Angle A = 180 ° – angle B – angle C = 180 ° – 90 ° – 60 ° = 90 ° – 60 ° = 30 °;

2) Consider the triangle ABB1.

Angle B1 = 90 °;

Angle A = 30 °;

sin A = BB1 / AB;

Let us express AB from here.

AB = BB1 / sin A;

Substitute the known values and calculate the leg AB of the triangle ABC.

AB = 2 cm / sin 30 ° = 2 cm / (1/2) = 2 cm * 2/1 = 2 * 2 cm = 4 cm.

This means that the leg of the triangle ABC is equal to AB = 4 cm.