In triangle ABC, angle C is 90 degrees. angle A is 30. AC = 19√3. find BC.

We find BC in the triangle abc if it is known:

Angle C is 90 °;
Angle A is 30 °;
AC = 19√3.

Solution:

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

We get the formula in the form:

tg A = BC / AC;

From here we will express BC.

ВС = tg A * AC;

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

We get:

ВС = tan 30 * 19√3 = √3 / 3 * 19√3 = 19/3 * √ (3 * 3) = 19/3 * √9 = 19/3 * 3 = 19/1 * 1 = 19;

As a result, we got that the leg BC = 19.