Question

8 in the accompanying diagram of right triangle abc ab = 8, bc = 15, ac = 17, and m∠abc = 90. what is tan∠c? 1) 8/15 2) 17/15 3) 8/17 4) 15/17

Explanation:

Step1: Recall the tangent formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle C\), the side opposite to \(\angle C\) is \(AB\) and the side adjacent to \(\angle C\) is \(BC\).

Step2: Substitute the values

We know that \(AB = 8\) and \(BC=15\). So, \(\tan\angle C=\frac{AB}{BC}\).
Substituting the values, we get \(\tan\angle C=\frac{8}{15}\).

Answer:

1. \(\frac{8}{15}\)