Question

13 right triangle abc has legs of 8 and 15 and a hypotenuse of 17, as shown in the diagram below. the value of the tangent of ∠b is 1) 0.4706 2) 0.5333 3) 0.8824 4) 1.8750

Explanation:

Step1: Recall the tangent formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle B\), the opposite side is \(AC = 8\) and the adjacent side is \(BC=15\).

Step2: Calculate \(\tan B\)

\(\tan B=\frac{AC}{BC}\)
Substitute \(AC = 8\) and \(BC = 15\) into the formula: \(\tan B=\frac{8}{15}\approx0.5333\)

Answer:

1. \(0.5333\)