Question

unit exam - right triangles and trigonometry
solve for x.
7 cm
37°
x = ? cm
round to the nearest hundredredth.

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with the opposite side to the 37° angle equal to 7 cm, and \(x\) is the hypotenuse. The sine function relates opposite and hypotenuse:
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

Substitute $\theta = 37^\circ$, opposite = 7, hypotenuse = $x$:
$\sin(37^\circ) = \frac{7}{x}$

Step3: Rearrange to solve for x

Isolate $x$ by cross-multiplying:
$x = \frac{7}{\sin(37^\circ)}$

Step4: Calculate the value

Use $\sin(37^\circ) \approx 0.6018$:
$x \approx \frac{7}{0.6018} \approx 11.63$

Answer:

11.63 cm