Question

solve for x.
37°
8 cm
x = ? cm
round to the nearest hundredth.

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle with angle \(37^\circ\), adjacent side \(8\) cm, and opposite side \(x\). Use tangent: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\)
\(\tan(37^\circ)=\frac{x}{8}\)

Step2: Solve for \(x\)

Multiply both sides by \(8\): \(x = 8\times\tan(37^\circ)\)
Calculate \(\tan(37^\circ)\approx0.7536\), so \(x\approx8\times0.7536\)
\(x\approx6.0288\)

Step3: Round to nearest hundredth

\(x\approx6.03\)

Answer:

\(6.03\)