Two trees in a park are 14.80 meters apart. An observer, whose eye line is 1.80 m above the ground, is standing halfway between the trees. The angles of elevation of the tops of the trees from the observer’s eye line are 17° and 23°. Determine the height of each tree to the nearest 0.01 m.

again, use tan. he adjacent leg in each case is 7.4

be sure to add 1.8 to the answers, since that's how high the observation point is.

To determine the height of each tree, we can use the concept of trigonometry.

Let's label the distance between the observer and each tree as x. Since the observer is standing halfway between the trees, the distance from the observer to each tree is x/2.

We can create two right triangles: one for each tree. Let's label the height of the first tree as h1 and the height of the second tree as h2.

In the first right triangle, we can use the angle of elevation of the first tree (17°) to relate the height of the first tree, h1, to the distance from the observer, x/2. We can use the tangent function, which relates the opposite side to the adjacent side.

Tangent(17°) = h1 / (x/2)

Similarly, in the second right triangle, we can use the angle of elevation of the second tree (23°) to relate the height of the second tree, h2, to the same distance from the observer, x/2.

Tangent(23°) = h2 / (x/2)

Now, solving these two equations simultaneously will help us find the values of h1 and h2.

First, rearrange the equation for the tangent of 17° to solve for h1:

h1 = Tangent(17°) * (x/2)

Next, rearrange the equation for the tangent of 23° to solve for h2:

h2 = Tangent(23°) * (x/2)

Now, let’s substitute the given values into the equation. The distance between the trees is 14.80 meters, and the observer’s eye line is 1.80 meters above the ground, so the distance from the observer to each tree is (14.80/2) = 7.40 meters.

Using a scientific calculator or an online trigonometric calculator, plug in the values for tangent(17°) and tangent(23°), then calculate h1 and h2:

h1 = Tangent(17°) * (7.40)
h2 = Tangent(23°) * (7.40)

After calculating these values, you will obtain the height of each tree, h1 and h2, to the nearest 0.01 meters.