Question

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.

Answer 1

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 =
`(14ft)/(7ft)`

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

Answer 2

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

Explanation:

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

SOH CAH TOA

sin θ =
`(opposite)/(hypotenuse)`

cosθ =
`(adjacent)/(hypotenuse)`

tan θ =
`(opposite)/(adjacent)`

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

Therefore, we are going to use the formula;

tan θ =
`(opposite)/(adjacent)`

tan θ =
`(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°