Question

solve for ( x ). round to the nearest tenth, if necessary.

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \(CDE\), we have a right angle at \(D\), angle at \(E\) is \(62^\circ\), and the side opposite to angle \(E\) is \(CD = 15\), and the side adjacent to angle \(E\) is \(DE=x\). We can use the tangent function, which is defined as \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan(62^\circ)=\frac{CD}{DE}=\frac{15}{x}\).

Step2: Solve for \(x\)

From \(\tan(62^\circ)=\frac{15}{x}\), we can rearrange the formula to solve for \(x\). Cross - multiplying gives us \(x=\frac{15}{\tan(62^\circ)}\).

We know that \(\tan(62^\circ)\approx1.8807\). Substituting this value into the formula: \(x = \frac{15}{1.8807}\approx7.976\). Rounding to the nearest tenth, we get \(x\approx8.0\).

Answer:

\(x\approx8.0\)