Question

1. consider this right triangle. find the length of side ab, to the nearest tenth.

Explanation:

Step1: Recall the tangent ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 43^{\circ}\), the opposite side to \(\theta\) is \(AB\) and the adjacent side is \(BC = 7\). So, \(\tan(43^{\circ})=\frac{AB}{7}\).

Step2: Solve for \(AB\)

Multiply both sides of the equation \(\tan(43^{\circ})=\frac{AB}{7}\) by \(7\). We get \(AB = 7\times\tan(43^{\circ})\).
Since \(\tan(43^{\circ})\approx0.9325\), then \(AB=7\times0.9325 = 6.5275\).

Answer:

\(6.5\)