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You are standing 20 feet away from a tree that is 45 feet tall. What is the angle of elevation to the top of the tree? (round to the nearest degree)

Sagot :

Consider the schematic diagram given below,

In the diagram, AB represents the height of the tree, and point C is the location of the observer.

The angle of of elevation to the top of the tree is the angle BCA here.

This angle can be calculated as,

[tex]\begin{gathered} \tan (\angle BCA)=\frac{AB}{BC} \\ \tan (\angle BCA)=\frac{45}{20} \\ \tan (\angle BCA)=2.25 \end{gathered}[/tex]

Taking the inverse function both sides,

[tex]\begin{gathered} \angle BCA=\tan ^{-1}(2.25) \\ \angle BCA\approx66^{\circ} \end{gathered}[/tex]

Thus, the required angle of elevation is approximately 66 degrees.

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