In a right-angled triangle ABC (angle C = 90 degrees), tg a = three quarters, if BC = 12, then the leg AC is …

In a right-angled triangle ABC it is known:

Angle C = 90 °;
tg a = 3/4;
BC = 12.

Find the AC leg.

tg a = BC / AC;

From here we express AC and get:

AC = BC / tg a;

Substitute the known values of the leg and tangent of angle A, find the leg adjacent to the angle a.

We get:

AC = 12 / (3/4) = 12/1 * 4/3 = 12 * 4/3 = 12/3 * 4 = 4 * 3/3 * 4 = 4 * 1/1 * 4 = 4 * 4 = sixteen;

As a result, we got that the leg of the triangle is AC = 16.

Answer: AC = 16.