Question

using trig to find a side
score: 2/5 penalty: 1 off
question
solve for x. round to the nearest tenth, if necessary.
answer attempt 1 out of 2
x =

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 58^{\circ}\), the opposite side to \(\theta\) is \(YT = 6.7\), and the adjacent side is \(YZ=x\). So, \(\tan(58^{\circ})=\frac{YT}{YZ}\).

Step2: Solve for \(x\)

Since \(\tan(58^{\circ})=\frac{6.7}{x}\), we can rewrite it as \(x=\frac{6.7}{\tan(58^{\circ})}\). We know that \(\tan(58^{\circ})\approx1.600334529\). Then \(x=\frac{6.7}{1.600334529}\).

Answer:

\(x\approx4.2\)