In a right-angled triangle ABC, the angle is C = 90. Find the length of the leg AC if the angle is B = 45, BC = 19.

In a right-angled triangle ABC, the following values are known:

Angle C = 90 °;
Angle = 45 °;
BC = 19.
Let’s find the length of the AC leg.

Decision:

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

tg a = BC / AC;

Let us express AC from here and get:

AC = BC / tg a;

Substitute the known values into the formula and calculate the value of the AC leg.

AC = 19 / tg 45 = 19 / (√2 / 2) = 19/1 * 2 / √2 = 19 * 2 / √2 = 38 / √2 = 38 * √2 / (√2 * √2) = 38√2 / √4 = 38√2 / 2 = 38/2√2 = 19 * √2 = 19√2;

As a result, we got that the leg AC = 19√2.

Answer: AC = 19√2.