Question

solve for x in the triangle. round your answer to the nearest tenth.
(there is a right triangle with one angle 67°, one leg length 20, hypotenuse x, and a box for x = )

Explanation:

Step1: Identify trigonometric ratio

The triangle is right - angled, and we know the opposite side to the \(67^{\circ}\) angle is \(20\), and \(x\) is the hypotenuse. So we use the sine function: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\), where \(\theta = 67^{\circ}\), opposite \( = 20\), and hypotenuse \(=x\). So \(\sin(67^{\circ})=\frac{20}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x=\frac{20}{\sin(67^{\circ})}\). Calculate \(\sin(67^{\circ})\approx0.9205\). Then \(x = \frac{20}{0.9205}\approx21.7\).

Answer:

\(21.7\)