A child lies on the ground and looks up at the top of a 14-ft tree nearby. The child is 7 ft away from the tree. What is the angle of elevation from the child to the top of the tree? Round to the nearest whole degree.

make the problem into a right triangle. The 14 ft as side a and the 7ft as side b

when a and b meet there is a 90° angle

To find the angle of elevation use Tangent Θ = \(\frac{14ft}{7ft}\)

Now to solve for Θ ; in your calculator do \(Tan^{-1}( \frac{14}{7})\) and it should come out to about 63.43494882 or 63.435°

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ummuabdallah ummuabdallah · Answer 2 · 2020-04-09T22:13:40-04:00

Answer:

The angle of elevation from the child to the top of the tree is 63°

Step-by-step explanation:

To solve this problem, we are simply going to use the trig.ratio formula

SOH CAH TOA

sin θ = \(\frac{opposite}{hypotenuse}\)

cosθ = \(\frac{adjacent}{hypotenuse}\)

tan θ = \(\frac{opposite}{adjacent}\)

We have our adjacent = 7 ft and opposite = 14 ft

Therefore, we are going to use the formula;

tan θ = \(\frac{opposite}{adjacent}\)

tan θ = \(\frac{14}{7}\)

tan θ = 2

We are going to take the \(tan^{-1}\) of both-side in order to get the value of θ

\(tan^{-1}\) tan θ = \(tan^{-1}\) 2

θ = 63.43

θ = 63°

Therefore, the angle of elevation from the child to the top of the tree is 63°