Question

Jill is standing 80 feet away from a tree. She can see the base of the treefrom an angle of depression of 10°. To see the top of the tree, she mustlook up to an angle of elevation of 35º. How tall is the tree? Round to thenearest one hundredth of a foot.

Answer 1

Given data:

The horizontal distance is AB=80 ft.

The figure for the given data is,

In traingle ABC, the expression for tan(35°) is,

`\begin{gathered} \text{tan}(35^(\circ))=(BC)/(AB) \\ BC=(80ft)tan(35^(\circ)) \\ =56.016\text{ ft} \end{gathered}`

In triangle ABD, the expression for tan(10°) is,

`\begin{gathered} \tan (10^(\circ))=(BD)/(AB) \\ BD=(80ft)tan(10^(\circ)) \\ =14.106\text{ ft} \end{gathered}`

The height of the tree is,

`\begin{gathered} H=BC+BD \\ =56.016\text{ ft + 14.106 ft} \\ =70.122\text{ ft} \\ \approx70.12\text{ ft} \end{gathered}`

Thus, the height of the tree is 70.12 ft