Question

solve for $x$. round to the nearest tenth, if necessary.
answer
attempt 1 out of 3
$x =$
submit answer
copyright ©2025 deltamath.com all rights reserved.
terms & policies
deltamath.com

Explanation:

Step1: Use trigonometric ratio

In right - triangle \( \triangle NOM\) with right - angle at \(N\), we know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 52^{\circ}\), the opposite side to \(\angle O\) is \(x\) (side \(MN\)) and the adjacent side to \(\angle O\) is \(ON = 7\). So, \(\tan O=\tan(52^{\circ})=\frac{x}{7}\).

Step2: Solve for \(x\)

Since \(\tan(52^{\circ})\approx1.2799\), then \(x = 7\times\tan(52^{\circ})\). Substitute the value of \(\tan(52^{\circ})\): \(x=7\times1.2799 = 8.9593\approx9.0\)

Answer:

\(x = 9.0\)