Question

question 31 (1 point)
what is the measure of db in the triangle shown?

a) 30°
b) 45°
c) 90°
d) 60°

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, we can use the cosine ratio. The cosine of an angle $\theta$ in a right - triangle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Let $\angle B=\theta$. The adjacent side to $\angle B$ is $\sqrt{3}$ and the hypotenuse is 2. So, $\cos\theta = \frac{\sqrt{3}}{2}$.

Step2: Recall the value of cosine

We know that $\cos30^{\circ}=\frac{\sqrt{3}}{2}$ and $\cos60^{\circ}=\frac{1}{2}$, $\cos45^{\circ}=\frac{\sqrt{2}}{2}$, $\cos90^{\circ}=0$.

Answer:

A. $30^{\circ}$