In triangle ABC, angle C is 90 °, AB = 20, AC = 12. Find sinA.

Given:

ABC – right triangle;

Angle C = 90 degrees;

AB = 20;

AC = 12;

Find sin a.

Decision:

In order to find leg BC, we use the Pythagorean theorem.

ВС = √ (AB ^ 2 – AC ^ 2);

To find sin a, use the formula sin a = BC / AB.

Substitute the known values into the formula for the sine of the angle a. We get:

sin a = BC / AB = BC / 20 = √ (AB ^ 2 – AC ^ 2) / 20 = √ (20 ^ 2 – 12 ^ 2) / 20 = √ (400 – 144) / 20 = √256 / 20 = 16/20 = (4 * 5) / (5 * 5) = 4/5 = 0.8;

As a result, we got sin a = 0.8.

Answer: AB = 6.25.