Question

1. determine side $x$.

1. in relation to angle 21 degrees, side $x$ = adjacent side and 2.600 centimeters side = opposite side.

Explanation:

Step1: Recall the tangent function

In a right triangle, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side. So, \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 21.00^\circ\), the opposite side is \(2.600\) cm, and the adjacent side is \(x\). So we have \(\tan(21.00^\circ)=\frac{2.600}{x}\).

Step2: Solve for \(x\)

We can rearrange the formula to solve for \(x\). From \(\tan(21.00^\circ)=\frac{2.600}{x}\), we get \(x=\frac{2.600}{\tan(21.00^\circ)}\).

First, calculate \(\tan(21.00^\circ)\). Using a calculator, \(\tan(21^\circ)\approx0.38386\).

Then, substitute the value into the formula: \(x = \frac{2.600}{0.38386}\approx6.773\) cm.

Answer:

\(x\approx6.77\) cm (or more precise \(6.773\) cm depending on the required precision)