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 = [tex] \frac{14ft}{7ft} [/tex]

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

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ummuabdallah ummuabdallah · Answer 2 · 2020-04-10T04:13:40+02:00

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 = [tex]\frac{opposite}{hypotenuse}[/tex]

cosθ = [tex]\frac{adjacent}{hypotenuse}[/tex]

tan θ = [tex]\frac{opposite}{adjacent}[/tex]

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

Therefore, we are going to use the formula;

tan θ = [tex]\frac{opposite}{adjacent}[/tex]

tan θ = [tex]\frac{14}{7}[/tex]

tan θ = 2

We are going to take the [tex]tan^{-1}[/tex] of both-side in order to get the value of θ

[tex]tan^{-1}[/tex] tan θ = [tex]tan^{-1}[/tex] 2

θ = 63.43

θ = 63°

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