Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 60^{\circ}$, the adjacent side to the $60^{\circ}$ angle is $x$, and the hypotenuse is $9$.
So, $\cos60^{\circ}=\frac{x}{9}$.

Step2: Solve for $x$

Since $\cos60^{\circ}=\frac{1}{2}$, we have the equation $\frac{1}{2}=\frac{x}{9}$.
Cross - multiply: $x = 9\times\frac{1}{2}$.
Calculate: $x = 4.5$.

Answer:

$4.5$