Question

solve for ( x ). round to the nearest tenth, if necessary.
triangle image with right angle at o, angle at p is 60°, hypotenuse pn = 9, and side po = x

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( PON \), \( \angle P = 60^\circ \), hypotenuse \( PN = 9 \), and adjacent side to \( 60^\circ \) is \( x \) (side \( PO \)). Use cosine: \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \).
\( \cos(60^\circ)=\frac{x}{9} \)

Step2: Solve for \( x \)

We know \( \cos(60^\circ) = 0.5 \), so substitute:
\( 0.5=\frac{x}{9} \)
Multiply both sides by 9: \( x = 9\times0.5 = 4.5 \)

Answer:

\( 4.5 \)