Question

In order to find the height of a cliff, you stand at the bottom of the cliff, walk 60 feet

from the base, and place a mirror on the ground. Then you face the cliff and step back
5 feet so that can see the top of the cliff in the mirror. Assuming your eyes are 6 feet
above the ground, explain how to use this information to find the height of the cliff.
(The angles marked congruent are congruent because of the nature of the reflection of
light in a mirror.)
Q5ft
60 ft
K
Mirror

Answer 1

Answer: 72 ft

Explanation:

We can solve this problem using geometry, if we draw two righ triangles (figure attached):

-One formed by you, assuming you are 6 ft tall, and the ground

-The other formed by the height of the cliff, the bottom of the cliff and the ground.

Both triangles are congruent, having the mirror as a common vertex, hence we can use the following relation to find :

`(6 ft)/(y)=(5 ft)/(60 ft)`

Isolating :

`y=((60 ft)(6 ft))/(5 ft)=72 ft` This is the height of the cliff