Question

solve for x in the triangle. round your answer to the nearest tenth. 6 37° x =

Explanation:

Step1: Identify trigonometric ratio

In the right triangle, the side opposite the \(37^\circ\) angle is \(6\), and \(x\) is the hypotenuse. We use the sine function: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So \(\sin(37^\circ)=\frac{6}{x}\).

Step2: Solve for \(x\)

Rearrange the formula: \(x = \frac{6}{\sin(37^\circ)}\). Calculate \(\sin(37^\circ)\approx0.6018\). Then \(x=\frac{6}{0.6018}\approx9.97\approx10.0\) (rounded to nearest tenth).

Answer:

\(x\approx10.0\)