Question

To estimate the height of a tree, one person positions himself due south of a tree and the other stands due east a tree. If the two people are the same distance from the tree and are 82 feet apart from each other, what is the height of the tree if the angle of elevation from the ground at each person’s position is 480?

Answer 1

The height of the tree is 223.6 feet.

Let x be the distance from each person to the tree and let h be the height of the tree. We have two right triangles with legs of length x and hypotenuses of length h. We are given that the angle of elevation from the ground at each person's position is 480. This means that the angle opposite the hypotenuse in each triangle is 480. We can use the tangent function to relate the sides of each triangle.

In the triangle with legs of length x and hypotenuse of length h, we have:

tan 480 = h/x

Solving for h, we get:

h = x * tan 480

We are also given that the two people are 82 feet apart from each other. This means that x + x = 82, or 2x = 82. Solving for x, we get:

x = 41

Now we can substitute this value of x into the equation for h:

h = 41 * tan 480

h = 41 * sqrt(3)

h ≈ 223.6 feet

Therefore, the height of the tree is approximately 223.6 feet.