Question

solve for ( x ). round to the nearest tenth, if necessary.

answer attempt 1 out of 2
( x = )
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Explanation:

Step1: Identify trigonometric ratio

We have a right triangle at Q. For angle $19^\circ$, side QR = 7.6 is adjacent, and side RP = $x$ is the hypotenuse. Use cosine: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(19^\circ)=\frac{7.6}{x}$

Step3: Rearrange to solve for $x$

$x=\frac{7.6}{\cos(19^\circ)}$

Step4: Calculate the value

First, $\cos(19^\circ)\approx0.9455$, so $x\approx\frac{7.6}{0.9455}\approx8.0$

Answer:

$x=8.0$