Question

Tim looks up at the top of a tree at an angle of elevation of 40 degrees. If heis 5 ft tall and 10 ft from the tree, how tall is the tree?

Answer 1

13.391 ft

Explanations:

The schematic diagram of the given question is shown below;

The height of the tree is expressed as:

H = h +5

Determine the value of h using the SOH CAH TOA identity

`\begin{gathered} tan\theta=(opposite)/(adjacent) \\ tan40^0=(h)/(10) \\ h=10tan40 \\ h=10(0.8391) \\ h=8.391ft \\ \end{gathered}`

Determine the height of the tree

`\begin{gathered} H=h+5 \\ H=8.391+5 \\ H=13.391ft \end{gathered}`

Hence the height of the tree is 13.391ft