Question

As shown in the diagram below, the angle ofelevation from a point on the ground to the top ofthe tree is 34º.

Answer 1

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:

`\begin{gathered} \tan \theta=(opposite)/(adjacent) \\ \text{with respect to the 34}^o,\text{ we have:} \\ \text{opposite}=h \\ \text{adjacent =20} \\ \text{Thus:} \\ \tan 34^o=(h)/(20) \\ 20*\tan 34^o=h \\ h=20*\tan 34^o \\ \sin ce\text{ }\tan 34^o=0.6745 \\ \text{Therefore:} \\ h=20*0.6745\text{ =13.49} \\ h=13.5ft\text{ (to the nearest tenth of a foot)} \end{gathered}`

Therefore, the height of the tree is 13.5 ft