Ann 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 35 ft from the tree, and Ann is standing 8.7 ft from the mirror, as shown in the figure. Her eyes are 6 ft above the ground. How tall is the tree? Round your answer to the nearest foot. (The figure is not drawn to scale.)

Answer 1

To find the height of the tree, we can use similar triangles.

1. Ann's eye level is 6 feet above the ground. If we denote the height of the tree as \( h \), the distance from Ann to the tree is \( d = 35 + 8.7 = 43.7 \) feet (35 feet from the mirror to the tree, plus 8.7 feet from Ann to the mirror).

2. We can set up a relationship using the heights and distances from the tree:

   \[ \frac{h}{35} = \frac{6}{8.7} \]

3. Cross-multiply to solve for \( h \):

   \[ h \cdot 8.7 = 6 \cdot 35 \]

   \[ h \cdot 8.7 = 210 \]

   \[ h = \frac{210}{8.7} \]

4. Now, calculate \( h \):

   \[ h \approx \frac{210}{8.7} \approx 24.14 \text{ feet} \]

5. Rounding to the nearest foot, the height of the tree is approximately:

   \[ \boxed{24} \text{ feet} \]