In triangle ABC, angle C = 90 sinB = 7/25 BC = 48 find AC.

Let’s find the cosine of angle B and its tangent:

cos B = (1 – sin2 B) ^ 0.5 = (1 – (7/25) 2) ^ 0.5 = (576/625) ^ 0.5 = 24/25.

tg B = sin B / cos B = (7/25) / 0.96 = 7/24.

By condition ABC is a right-angled triangle in which the angle is C = 90 °. That is, AC and BC are legs in a right-angled triangle ABC. Moreover, the first of them lies opposite the corner B, and the second is adjacent. Hence,

AC / BC = tan B, whence we obtain that

AC = BC * tg B = 48 * 7/24 = 14.

Answer: AC = 14.