The height of the tree can be found as follows:
Step 1: Make a well labelled sketch of the situation, in mathematical terms, as below:
Step 2: Apply the appropriate trigonometric ratio that will help solve for the unknown side of the triangle, as follows:
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \text{with respect to the 34}^o,\text{ we have:} \\ \text{opposite}=h \\ \text{adjacent =20} \\ \text{Thus:} \\ \tan 34^o=\frac{h}{20} \\ 20\times\tan 34^o=h \\ h=20\times\tan 34^o \\ \sin ce\text{ }\tan 34^o=0.6745 \\ \text{Therefore:} \\ h=20\times0.6745\text{ =13.49} \\ h=13.5ft\text{ (to the nearest tenth of a foot)} \end{gathered}[/tex]
Therefore, the height of the tree is 13.5 ft
