Question

solve for x. round to the nearest tenth, if necessary.
right triangle with right angle at o, angle at p is 69 degrees, side po is 80, side no is x
answer attempt 1 out of 2
x = blank box submit answer

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \(NOP\), we know angle \(P = 69^\circ\), opposite side to angle \(P\) is \(x\) ( \(NO = x\) ), and adjacent side to angle \(P\) is \(OP = 80\). We use the tangent function, which is \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). So \(\tan(69^\circ)=\frac{x}{80}\).

Step2: Solve for \(x\)

Multiply both sides by \(80\) to get \(x = 80\times\tan(69^\circ)\). Calculate \(\tan(69^\circ)\approx2.605\). Then \(x = 80\times2.605 = 208.4\).

Answer:

\(x = 208.4\)