You are 6 feet tall and cast a shadow 4 feet long. At the same time, a nearby building casts a shadow 15 feet 4 inches long. Find the height of the building.

Answer 1

Let's first convert the shadow of the building from feet and inches to just inches for consistency.

15 feet 4 inches can be written as 15 * 12 + 4 = 184 inches.

Using similar triangles, we can set up the proportion:

Height of building / Length of building's shadow = Your height / Your shadow length

Let x be the height of the building.

Therefore, x / 184 inches = 6 feet / 4 feet.

Converting 6 feet to inches: 6 * 12 = 72 inches.

Simplifying the proportion: x / 184 = 72 / 4.

Cross-multiplying, we have:
4x = 184 * 72,
4x = 13,248.

Dividing both sides by 4, we get:
x = 13,248 / 4,
x = 3,312 inches.

The height of the building is 3,312 inches.