A man is sitting by a pool. He looks up at an angle of elevation of 18 degrees at a bird in a nest at the top of a tall tree. Since the man is 200 feet from the bird's tree. How tall is the tree?

looks like simple tangent

tan 18° = height/200
height = 200tan18° = 64.98 or appr 65 ft

To find the height of the tree, we can use trigonometry. Let's draw a diagram to help visualize the problem.

B (bird)
/|
/ | h (height of tree)
/ |
/ |
/ |
/ |
/18° | \
/ | \
/________| \
A C D (man)

In the diagram, line AB represents the height of the tree (h), line AC represents the distance from the man to the base of the tree (200 ft), line BC represents the distance from the bird to the base of the tree (unknown), and angle CAB is the angle of elevation (18°).

We can use the tangent function to solve for BC. The tangent of an angle is the ratio of the opposite side to the adjacent side. In this case, the opposite side is BC, and the adjacent side is AC. So we have:

tan(18°) = BC / AC

We can rearrange this equation to solve for BC:

BC = tan(18°) * AC

Now we can substitute the known values:

BC = tan(18°) * 200

Using a calculator, we can find the value of tan(18°), which is approximately 0.3249. Substituting that value, we get:

BC ≈ 0.3249 * 200
BC ≈ 64.98 ft

So the height of the tree, AB, is approximately 64.98 feet.