Question

what is the measure of angle b in the figure?

Explanation:

Step1: Identify the triangle type

It's a right - triangle with sides 1, $\sqrt{3}$, and 2 (by Pythagorean theorem $1^{2}+(\sqrt{3})^{2}=2^{2}$).

Step2: Use trigonometric ratio

We know that $\sin B=\frac{AC}{BC}$. Given $AC = 1$ and $BC = 2$, so $\sin B=\frac{1}{2}$.

Step3: Find the angle

Since $\sin B=\frac{1}{2}$ and $B$ is an acute angle in a right - triangle, $B = 30^{\circ}$.

Answer:

$30^{\circ}$