In triangle ABC, the angle b is equal to 120 degrees. Find the side AB if the height an is 9 cm.

In the ABC triangle it is known:

Angle B = 120 °;
Height BH = 9 cm.

Let’s find the AB side.

Solution:

Consider a triangle ABH with a right angle H.

Angle B = 120 ° / 2 = 60 °;

Then the angle A = 30 °.

It is known that BH = 9 cm.

Then we find the side AB.

sin A = BH / AB;

From here we express BН.

AB = BH / sin A;

Substitute the known values and calculate the AB side.

AB = 9 / sin 30 = 9 / (1/2) = 9 * 2/1 = 9 * 2 = 18;

As a result, we got that the side AB of the triangle ABC is 18 cm.

Answer: AB = 18 cm.