Question

find x using the right triangle shown. round your answer to the nearest tenth. (trigonometric ratios) 5 points

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle with hypotenuse \( 19 \), angle \( 71^\circ \), and \( x \) as the adjacent side to the angle. So we use cosine: \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \)
\( \cos(71^\circ)=\frac{x}{19} \)

Step2: Solve for \( x \)

Multiply both sides by \( 19 \): \( x = 19\times\cos(71^\circ) \)
Calculate \( \cos(71^\circ)\approx0.3256 \)
\( x\approx19\times0.3256 \approx 6.2 \)

Answer:

\( 6.2 \)