Question

A man is in a treehouse 10 feet above the ground. He is looking at the top of another tree that is 22 feet tall.The bases of the trees are 30 feet apart. What is the angle of elevation from the man's feet to the top of the tree? Round to the nearest degree.

Answer 1

Answer:

22 degrees.

Step-by-step explanation:

Please find the attachment.

We have been given that a man is in a tree-house 10 feet above the ground. He is looking at the top of another tree that is 22 feet tall.The bases of the trees are 30 feet apart.

To find the angle of elevation from the man's feet to the top of the tree, we will use tangent because we know adjacent side and opposite side to angle x.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(x)=\frac{12}{30}$

Now, we will use arctan or inverse tan to solve for x as:

$x=\text{tan}^{-1}(\frac{12}{30})$

$x=21.8014094^{\circ}$

Upon rounding to nearest degree, we will get:

$x\approx 22^{\circ}$

Therefore, the angle of elevation from the man's feet to the top of the tree is approximately 22 degrees.