Question

the equation tan(58°) = 18/b can be used to find the length of ac. what is the length of ac? round to the nearest tenth.

Explanation:

Step1: Recall the tangent - ratio formula

In right - triangle \(ABC\) with right angle at \(C\), \(\tan(A)=\frac{BC}{AC}\). Given \(A = 58^{\circ}\) and \(BC = 16\) cm, and the formula \(\tan(58^{\circ})=\frac{16}{AC}\).
We know that \(\tan(58^{\circ})\approx1.60033\). So, \(1.60033=\frac{16}{AC}\).

Step2: Solve for \(AC\)

Cross - multiply to get \(AC\times1.60033 = 16\). Then, \(AC=\frac{16}{1.60033}\).
Calculating \(\frac{16}{1.60033}\approx9.997\approx10.0\) cm.

Answer:

10.0 cm