Question

which equation can be used to solve for b?

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Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Identify the sides relative to the given angle

For angle \(A = 30^{\circ}\), the side opposite to angle \(A\) is \(BC = 5\) cm and the side adjacent to angle \(A\) is \(AC=b\).

Step3: Apply the tangent ratio

Using \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), with \(\theta = 30^{\circ}\), opposite \(=5\) and adjacent \(=b\), we get \(\tan(30^{\circ})=\frac{5}{b}\).

Answer:

\(\tan(30^{\circ})=\frac{5}{b}\) (the first option)