Question

solve for x. round to the nearest tenth, if necessary.
(image of a right triangle nop with right angle at o, angle at p is 69 degrees, side op is 80, side no is x)

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 69^{\circ}\), the opposite side to \(\theta\) is \(x\) and the adjacent side is \(80\). So, \(\tan(69^{\circ})=\frac{x}{80}\).

Step2: Solve for \(x\)

We know that \(\tan(69^{\circ})\approx2.605\). Then \(x = 80\times\tan(69^{\circ})\). Substitute \(\tan(69^{\circ})\approx2.605\) into the equation: \(x\approx80\times2.605\).

Answer:

\(x\approx208.4\)