Question

use the following diagram to answer question 1.

1. find the value of side x to one decimal place.

hint: \\( \theta = \\)
\\( \text { opposite } = \\)
\\( \text { adjacent } = \\)
\\( \text { trig ratio used: } \\)

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the tangent of an angle \(\theta\) is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 17^{\circ}\), the side opposite to the \(17^{\circ}\) angle is \(13.2\) m, and the side adjacent to the \(17^{\circ}\) angle is \(x\). So, \(\tan(17^{\circ})=\frac{13.2}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation \(\tan(17^{\circ})=\frac{13.2}{x}\) as \(x=\frac{13.2}{\tan(17^{\circ})}\).
We know that \(\tan(17^{\circ})\approx0.3057\).
Then \(x=\frac{13.2}{0.3057}\approx43.2\)

Answer:

\(x\approx43.2\)