In triangle ABC, angle C is 90 °, AB = 30, AC = 24. Find sin A. How to solve this type of problem?

If the angle C is 90 degrees, then the rectangle ABC is rectangular. The side that lies opposite the corner C is called the hypotenuse. In our triangle, this is side AB and it is equal to 30. The other two sides are called legs. We have these sides BC and AC = 24.

Now let’s answer the question, is the sine of an angle? The sine of the angle is the ratio of the opposite leg to the hypotenuse. Consider our triangle. For angle A, leg BC will be opposite. This leg is still unknown to us, but we know the adjacent leg AC = 24.

To find the BC leg, we use the Pythagorean theorem.

AB ^ 2 = BC ^ 2 + AC ^ 2 hence, BC ^ 2 = AB ^ 2 – AC ^ 2

BC ^ 2 = 30 ^ 2 – 24 ^ 2 = 900 – 576 = 324

BC = √ 324 = 18

sin A = BC: AB

sin A = 18: 30 = 0.6.

Answer: sin A = 0.6.