Amie who is 5.4 feet tall wants to find the length of a building. She walks 42.8 feet from the base of the building along the shadow of the building until her head is in a position where the tip of her shadow exactly overlaps in the end of the building top's shadow. She is now 7.2 feet from the end of the shadow. How tall is the building?

Question

Amie who is 5.4 feet tall wants to find the length of a building. She walks 42.8 feet from the base of the building along the shadow of the building until her head is in a position where the tip of her shadow exactly overlaps in the end of the building top's shadow. She is now 7.2 feet from the end of the shadow. How tall is the building?

Answer 1

To solve this problem, we can use similar triangles.

Let x be the height of the building.

When Amie stands at the base of the building, her shadow and the building's shadow form one set of similar right triangles. The ratio of Amie's height to her shadow is the same as the ratio of the building's height to its shadow.

So, we have:

5.4 feet / 42.8 feet = x / 7.2 feet

Now, we can solve for x:

5.4 / 42.8 = x / 7.2

x = (5.4 / 42.8) * 7.2
x = 0.1261682243 * 7.2
x = 0.9072 feet

Therefore, the building is approximately 0.9072 feet tall.