Question

susan is flying a kite, which gets caught in the top of a tree. use the diagram to estimate the height of the tree.

Explanation:

Step1: Use trigonometric ratio

We know that in a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 44^{\circ}\), the adjacent side \(x = 90\) feet and the opposite side \(y\) is the height of the tree. So, \(\tan(44^{\circ})=\frac{y}{90}\).

Step2: Solve for \(y\)

We know that \(\tan(44^{\circ})\approx0.9657\). Then \(y = 90\times\tan(44^{\circ})\). Substituting the value of \(\tan(44^{\circ})\), we get \(y=90\times0.9657 = 86.913\approx87\) feet.

Answer:

\(87\) ft