Question

1. jill stands 17m from a tree. the angle of elevation from her feet to the top of the tree measures 58°. calculate the height of the tree. express your final answer in a concluding statement, with units, correct to one decimal place. (5 marks)

Explanation:

Step1: Use the tangent function

We know that in a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 58^{\circ}\), the adjacent side \(x = 17\)m (distance from Jill to the tree), and the opposite side \(y\) (height of the tree) is what we want to find. So, \(\tan(58^{\circ})=\frac{y}{17}\).

Step2: Solve for \(y\)

$$
LATEXBLOCK0
$$

Step3: Round to one decimal place

Rounding \(27.20568699\) to one decimal place gives \(y\approx27.2\)

Answer:

The height of the tree is approximately \(27.2\)m.