Question

1. determine side $x$.

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the opposite side to the angle \(21.00^\circ\) (assuming it's a degree measure) is \(2.600\) cm, and \(x\) is the adjacent side. The tangent function relates the opposite and adjacent sides: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan(21^\circ)=\frac{2.600}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = \frac{2.600}{\tan(21^\circ)}\). Calculate \(\tan(21^\circ)\approx0.3839\). Then \(x=\frac{2.600}{0.3839}\approx6.77\) cm.

Answer:

\(x\approx6.77\) cm (depending on the precision of \(\tan(21^\circ)\) used, the answer may vary slightly)