Question

in the right triangle, one angle is 39°, the length of the vertical side is 17, and the length of the horizontal side is x. we need to find the value of x.

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle with angle \(39^\circ\), opposite side \(x\), and adjacent side \(17\). So we use the tangent function: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\)
\(\tan(39^\circ)=\frac{x}{17}\)

Step2: Solve for \(x\)

Multiply both sides by \(17\): \(x = 17\times\tan(39^\circ)\)
Calculate \(\tan(39^\circ)\approx0.8098\), then \(x\approx17\times0.8098\)
\(x\approx13.7666\)

Answer:

\(x\approx13.77\) (rounded to two decimal places)