Question

A child lies on the ground and looks up at the top of a 17-ft tree nearby. The child is 14 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.

1) 35��
2) 55��
3) 51��

Answer 1

The angle of elevation from the child to the top of the tree is approximately 51^\circ. (Option 3)

The correct option is 3.

Step-by-step explanation:

To find the angle of elevation (θ) from the child to the top of the tree, you can use the tangent function. The tangent of an angle in a right-angled triangle is the ratio of the opposite side to the adjacent side.

tan(θ) = opposite / adjacent

In this case:

tan(θ) = height of the tree / distance from the tree

tan(θ) = 17 / 14

Now, use the arctangent (inverse tangent) function to find (θ):

θ = arctan 17 / 14

Using a calculator, you get approximately 51.7^\circ.

Rounded to the nearest whole degree, the angle of elevation is θ ≈ 52^\circ .

So, the closest answer from the options is:

3) 51^\circ.

The correct option is 3.