Question

answer the following questions, showing all your work for full marks.

1. use the following diagram to answer question 1.
2. find the value of side ( x ) to one decimal place.

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

Explanation:

Step1: Identify trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 17^{\circ}\), the side opposite to \(\theta\) is \(13.2\) m, and the side adjacent to \(\theta\) is \(x\). So the trigonometric ratio used is \(\tan\).

Step2: Set up the equation

We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Substituting \(\theta = 17^{\circ}\), opposite \(=13.2\) m and adjacent \(=x\), we get \(\tan(17^{\circ})=\frac{13.2}{x}\).

Step3: Solve for \(x\)

Since \(x=\frac{13.2}{\tan(17^{\circ})}\). We know that \(\tan(17^{\circ})\approx0.3057\). Then \(x=\frac{13.2}{0.3057}\approx43.2\)

Answer:

\(x\approx43.2\) m.