Question

find the value of each trig ratio. evaluate tan x for the right triangle shown. type your answer in the boxes

Explanation:

Step1: Recall the tangent formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\tan X\), the side opposite to angle \(X\) is \(YZ = 12\), and the side adjacent to angle \(X\) is \(XY=9\).

Step2: Calculate \(\tan X\)

Using the formula \(\tan X=\frac{YZ}{XY}\), substitute \(YZ = 12\) and \(XY = 9\). So, \(\tan X=\frac{12}{9}=\frac{4}{3}\).

Answer:

\(\frac{4}{3}\)