Question

question 12 (1 point)
what is the measure of \\( \angle b \\) in the triangle shown?

a) \\( 30 ^ { \circ } \\)
b) \\( 60 ^ { \circ } \\)
c) \\( 45 ^ { \circ } \\)
d) \\( 90 ^ { \circ } \\)

Explanation:

Step1: Use the cosine function

In a right - triangle, \(\cos B=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to angle \(B\) is \(\sqrt{3}\) and the hypotenuse is \(2\). So, \(\cos B=\frac{\sqrt{3}}{2}\).

Step2: Find the angle

We know that if \(\cos\theta = \frac{\sqrt{3}}{2}\), then \(\theta = 30^{\circ}\) (since \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\)).

Answer:

A. \(30^{\circ}\)