In triangle ABC, angle C is 90 degrees, angle A is 60 degrees, AB is 18 cm. Find AC.

In the ABC triangle it is known:

Angle C = 90 °;
Angle A = 60 °;
AB = 18 cm.
Find the AC leg.

Solution:

If the hypotenuse and angle A are known, then we can find the AC leg.

In order to find the leg AC of the triangle ABC, we use the formula:

cos A = AC / AB.

Hence, AC = AB * cos A;

Substitute the known values into the formula and find the AC leg.

AC = 18 * cos 60 ° = 18 * 1/2 = 18/2 = 9;

From this, we got that the leg of the triangle is AC = 9.

Answer: AC = 9.