Question

find the exact value of sin b in simplest radical form.
(image of triangle bcd with right angle at c, bc=9, bd=12, cd=√63)
answer attempt 1 out of 3

Explanation:

Step1: Recall sine definition

In a right triangle, $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle B$, opposite side is $CD = \sqrt{63}$, hypotenuse is $BD = 12$.

Step2: Simplify $\sqrt{63}$

$\sqrt{63} = \sqrt{9\times7} = 3\sqrt{7}$.

Step3: Compute $\sin B$

$\sin B = \frac{\sqrt{63}}{12} = \frac{3\sqrt{7}}{12} = \frac{\sqrt{7}}{4}$.

Answer:

$\frac{\sqrt{7}}{4}$