In triangle ABC, angle C = 90 degrees, AB + 20 cm, BC = 12. Find the sine of angle B

The sine of an acute angle of a right triangle is the ratio of the opposite leg to the hypotenuse:

sin B = AC / AB.

To do this, you need to find the length of the second leg of the AC. Since the triangle is rectangular, we apply the Pythagorean theorem for the calculation:

AB ^ 2 = BC ^ 2 + AC ^ 2;

AC ^ 2 = AB ^ 2 – BC ^ 2;

AC ^ 2 = 20 ^ 2 – 12 ^ 2 = 400 – 144 = 256;

AC = √256 = 16 cm.

Now you can find the sine of angle B:

sin B = 16/20 = 4/5 = 0.5.

Answer: The sine of angle B is 0.8.