Question

16 10.5 14.2 12.9 x 10 51° version 1: pythagorean tripl

Explanation:

Step1: Identify the trigonometric relation

We have a right - triangle with an angle of \(51^{\circ}\), the opposite side to the angle is \(10\), and \(x\) is the hypotenuse. We use the sine function, which is defined as \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(51^{\circ})=\frac{10}{x}\).

Step2: Solve for \(x\)

From \(\sin(51^{\circ})=\frac{10}{x}\), we can re - arrange the formula to solve for \(x\). Cross - multiplying gives us \(x=\frac{10}{\sin(51^{\circ})}\). We know that \(\sin(51^{\circ})\approx0.7771\) (using a calculator). Then \(x = \frac{10}{0.7771}\approx12.87\).

Answer:

\(x\approx12.9\) (or more precisely, approximately \(12.87\))