Question

which equation can be used to solve for b?

Explanation:

Step1: Identify the trigonometric relation

Since it is a right - triangle and we know an angle and the hypotenuse, and we want to find the adjacent side to the given angle, we use the cosine function. The cosine of an angle in a right - triangle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos(A)=\frac{b}{AB}$

Step2: Substitute the values

We know that $A = 30^{\circ}$ and $AB = 10$ cm. Substituting these values into the cosine formula, we get $\cos(30^{\circ})=\frac{b}{10}$.

Answer:

$\cos(30^{\circ})=\frac{b}{10}$