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. a. 87 ft b. 74 ft c. 65 ft d. 63 ft

Answer 1

Given the information on the picture, we have the following right triangle:

we can use the tangent trigonometric function to find the height of the tree:

`\begin{gathered} tan(44)=\frac{\text{opposite side}}{adjacent\text{ side}}=(h)/(90) \\ \Rightarrow\tan (44)=(h)/(90) \end{gathered}`

solving for h, we get:

`\begin{gathered} (h)/(90)=\tan (44) \\ \Rightarrow h=90\cdot\tan (44)=86.9\approx87 \\ h=87ft \end{gathered}`

therefore, the height of the tree is 87 ft