In triangle ABC, angle C is 90 degrees, angle B is 30 degrees, BC = 3√3. Find AC?

In the triangle ABC, the following values of the triangle are known:

Angle C = 90 °;
Angle B = 30 °;
BC leg = 3√3.
Find the second leg of the AC.

The ratio of the opposite leg to the adjacent leg is equal to the tangent of the angle.

We get the formula in the form:

tg a = BC / AC;

Let us express AC from here.

AC = BC / tg a;

Substitute the known values of the leg and tangent of the angle, then we calculate the value of the second leg.

AC = 3√3 / tan 30 ° = 3√3 / (√3 / 3) = 3 * √3 * 3 / √3 = 3 * 3 * √3 / √3 = 9 * √3 / √3 = 9 * 1/1 = 9;

As a result, we got that the second leg of the rectangle is AC = 9.

Answer: AC = 9.