In triangle ABC, angle c is 90, angle A = 30, AB = √3. Find AC.

In the ABC triangle it is known:

Angle C is 90 °;
angle A = 30 °;
Hypotenuse AB = √3.
Let’s find the AC.

The cosine of angle A is equal to the ratio of the adjacent leg to the hypotenuse.

AC is the adjacent leg in relation to angle A.

AB – hypotenuse.

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

We get the formula in the form:

cos a = AC / AB;

Let us express from the formula AC.

AC = AB * cos a;

Substitute the known values and calculate the AC.

AC = √3 * cos 30 ° = √3 * 1/2 = √3 / 2;

As a result, we got that the leg of the triangle ABC is equal to AC = √3 / 2.