Question

1. in triangle abc; the angle c is a right angle,

$\cos a = \frac{\sqrt{31}}{3}$. what is $\sin b$?
a. $\frac{\sqrt{31}}{3}$
b. $\frac{\sqrt{31}}{2}$
c. $\frac{3}{\sqrt{31}}$
d. $\frac{2}{3}$

Explanation:

Step1: Use right triangle angle sum

In right triangle ABC, $\angle A + \angle B = 90^\circ$, so $\angle B = 90^\circ - \angle A$.

Step2: Apply co-function identity

$\sin B = \sin(90^\circ - A) = \cos A$.

Step3: Substitute given $\cos A$

$\sin B = \frac{\sqrt{31}}{3}$

Answer:

A. $\frac{\sqrt{31}}{3}$