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.
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.
To find the height of the building, we can create a proportion using the lengths of the shadows.
The height of the building will be the unknown variable (let's call it H).
Let's convert all the measurements to the same units. Since the shadow of the person is given in feet and the shadow of the building is given in feet and inches, let's convert the inches to feet.
1 foot is equal to 12 inches, so 4 inches can be expressed as 4/12 = 1/3 feet.
Now we have the following two proportions:
Height of the person / Length of the person's shadow = Height of the building / Length of the building's shadow
6 feet / 4 feet = H / (15 feet + 1/3 feet)
Next, we can simplify the equation:
6/4 = H / 15 1/3
Cross-multiplying, we get:
6 * 15 1/3 = 4 * H
To calculate 15 1/3, we can convert it to an improper fraction:
15 1/3 = (15 * 3 + 1)/3 = 46/3
Substituting this back into the equation, we have:
6 * (46/3) = 4 * H
Simplifying further, we have:
(6 * 46) / 3 = 4 * H
276/3 = 4 * H
92 = 4 * H
Now we can solve for H by dividing both sides of the equation by 4:
92/4 = H
H = 23
Therefore, the height of the building is 23 feet.