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: Identify the trig - function

We have a right - triangle where the adjacent side to the given angle is 90 feet and we want to find the opposite side (height of the tree). We use the tangent function, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Substitute the values

Given $\theta = 44^{\circ}$ and adjacent = 90 feet. So, $\tan(44^{\circ})=\frac{h}{90}$, where $h$ is the height of the tree. Then $h = 90\times\tan(44^{\circ})$.

Step3: Calculate the value

We know that $\tan(44^{\circ})\approx0.9657$. So, $h=90\times0.9657 = 86.913\approx87$ feet.

Answer:

87 ft