Question

To find the height of the Eiffel Tower, Kaylan placed a mirror 550 m away from the tower. She then positions herself as shown so that the top of the tower is visible in the mirror. She is standing 2.75 m from the mirror and her eyes are 1.8 m off the ground. How tall is the tower?

Answer 1

To find the height of the Eiffel Tower, we can use similar triangles. Let h be the height of the tower, as shown in the diagram below:

```

A B

|--------|-----------------|

| x |

| *--------C

| | |

| | h |

| | |

D--------*--------|

| y |

| | |

| | |

|--------|--------|

Kaylan

```

Triangle ABC is similar to triangle ABD, so we can set up the following proportion:

h / x = (h + 1.8) / y

We can solve for h by cross-multiplying and simplifying:

y * h = x * (h + 1.8)

y * h = x * h + 1.8x

h * (y - x) = 1.8x

h = 1.8x / (y - x)

We are given that Kaylan is standing 2.75 m from the mirror, so x = 2.75 m. We are also given that the mirror is 550 m away from the tower, so y = 550 m. Substituting these values into the equation for h, we get:

h = 1.8 * 2.75 / (550 - 2.75) = 0.033 m

Therefore, the height of the Eiffel Tower is approximately 0.033 km, or 33 meters.