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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?

Sagot :

Answer:

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

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

Determine the height of the tree

[tex]\begin{gathered} H=h+5 \\ H=8.391+5 \\ H=13.391ft \end{gathered}[/tex]

Hence the height of the tree is 13.391ft

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