Mark wanted to measure the height of a nearby building. He placed a mirror on the pavement at point P, 80 feet from the base of the building. He then backed away until he saw an image on the top of the building in the mirror. If Mark is 6 feet tall, and he is standing 9 feet from the mirror, how tall is the building?
you will have 2 similar triangles
then use the ratio ...
h/80 = 6/9 to solve for h
To find the height of the building, we can use similar triangles and the concept of triangulation. Let's break down the problem step by step:
1. Draw a diagram: Draw the building, the mirror, Mark, and the distances involved.
2. Identify the similar triangles: We have two similar triangles in the diagram. One triangle has sides consisting of Mark's height, his distance from the mirror, and the height of the building. The other triangle has sides made up of Mark's height, his distance from the mirror, and the distance from the mirror to the base of the building.
3. Set up proportions: Since the triangles are similar, we can set up a proportion based on the corresponding sides. Let's call the height of the building "h". The proportion will be:
Mark's height / Mark's distance = h / (Mark's distance + distance from mirror to building)
Plugging in the given values, we have:
6 feet / 9 feet = h / (9 feet + 80 feet)
4. Solve the proportion: Cross multiply and solve for "h".
6 feet * (9 feet + 80 feet) = h * 9 feet
6 feet * 89 feet = h * 9 feet
534 feet = 9h feet
h = 534 feet / 9 feet
h = 59.33 feet (rounded to two decimal places)
Therefore, the height of the building is approximately 59.33 feet.