if a 36-inch yardstick casts a 21-inch shadow, how tall is a building whose shadow is 168 feet
36 / 21 = h / 168
so
h = 168 (12 / 7)
To determine the height of the building, we can set up a proportion using the information from the yardstick and its shadow:
The height of the yardstick is 36 inches, and its shadow is 21 inches.
So, the ratio of height to shadow is 36 inches : 21 inches.
To find the height of the building, let's call it "h", and the shadow length, let's call it "s". The proportion can be set up as follows:
36 inches / 21 inches = h / s
Now, we can use the proportion to find the height of the building. Since the shadow of the building is given in feet, we need to convert the units to inches for consistency.
1 foot is equal to 12 inches. Thus, 168 feet is equal to 168 x 12 = 2016 inches.
Now, we can plug in the values into the proportion:
36 inches / 21 inches = h / 2016 inches
To solve for "h", we can cross-multiply:
(36 inches * 2016 inches) = (21 inches * h)
72,576 inches = 21 inches * h
Divide both sides by 21 inches to isolate "h":
h = 72,576 inches / 21 inches
Calculating this division:
h ≈ 3,460.57 inches
Therefore, the height of the building, when its shadow measures 168 feet, is approximately 3,460.57 inches.