Question

Donna wants to measure the height of a tree. She sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 37ft from the tree, and Donna is standing 6.6ft from the mirror, as shown in the figure. Her eyes are 6ft above the ground. How tall is the tree? Round your answer to the nearest foot. (The figure is not drawn to scale.)

Answer 1

Using similar triangles, we can set up the following proportion:

(tree height + Donna's height) / (distance from Donna to mirror) = Donna's height / (distance from mirror to top of tree)

Let h be the height of the tree.

Then we have:

(h + 6) / 6.6 = 6 / (37 + h)

Multiplying both sides by (37 + h) and simplifying, we get:

h + 6 = 222 / 6.6 - h / 6.6

Multiplying both sides by 6.6 and simplifying, we get:

6.6h + 39.6 = 222 - h

Solving for h, we get:

7.6h = 182.4

h = 24

Therefore, the height of the tree is approximately 24 feet.