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,
[tex]\begin{gathered} \text{tan}(35^{\circ})=\frac{BC}{AB} \\ BC=(80ft)tan(35^{\circ}) \\ =56.016\text{ ft} \end{gathered}[/tex]In triangle ABD, the expression for tan(10°) is,
[tex]\begin{gathered} \tan (10^{\circ})=\frac{BD}{AB} \\ BD=(80ft)tan(10^{\circ}) \\ =14.106\text{ ft} \end{gathered}[/tex]The height of the tree is,
[tex]\begin{gathered} H=BC+BD \\ =56.016\text{ ft + 14.106 ft} \\ =70.122\text{ ft} \\ \approx70.12\text{ ft} \end{gathered}[/tex]Thus, the height of the tree is 70.12 ft
