In triangle ABC, angle C = 90 degrees. BC = √21, AB = 5. Find sin B.

1. By the condition of the problem, it is known that in a right-angled triangle AB = 5, BC = √21.

By definition, the ratio of the adjacent leg to the hypotenuse is the cosine of an acute angle.

Let’s calculate the ratio of BC to AB in this triangle.

BC: AB = √21: 5, and this ratio will be the cosine of the angle B.

2. Using the well-known trigonometric formula, we find the sine of the angle B.

cos² + sin² = 1, hence sin² B = 1 – cos² B

Then sin B = √1 – cos² B = √1 – 21: 25 = √ (25 – 21): 25 = √4 / 25 = 2/5.

Answer: Sin B is 2/5.