Question

calculate the value of x. round to the nearest hundredth.
17.3
37°
x
21
21.66
22

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with angle $37^\circ$, adjacent side $17.3$, and hypotenuse $x$. Use cosine: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(37^\circ)=\frac{17.3}{x}$

Step3: Rearrange to solve for $x$

$x=\frac{17.3}{\cos(37^\circ)}$

Step4: Calculate the value

Use $\cos(37^\circ)\approx0.7986$, so $x\approx\frac{17.3}{0.7986}\approx21.66$

Answer:

21.66