A yardstick casts a shadow of 24 in. at the same time a telephone pole casts a shadow of 20 ft 8 in. What is the height of the telephone pole, to the nearest inch? (1 yd = 36 in., and 1 ft = 12 in.)
36/24 = x/248
Cross multiply and solve for x.
24x = 8,928
x = 372 inches
First, we need to convert the length of the yardstick's shadow from inches to feet. We know that 1 yardstick is equal to 36 inches. So, the length of the yardstick's shadow is 24 inches. To convert this to feet, we divide by 12 since there are 12 inches in 1 foot.
Length of yardstick's shadow in feet = 24 inches / 12 = 2 feet
Next, we need to convert the length of the telephone pole's shadow from feet and inches to just inches. The length of the telephone pole's shadow is 20 feet 8 inches. To convert this to inches, we multiply the number of feet by 12 and add the number of inches.
Length of telephone pole's shadow in inches = (20 feet * 12) + 8 inches = 240 inches + 8 inches = 248 inches
Now, we can set up a proportion to find the height of the telephone pole. The height of the telephone pole is to the length of its shadow as the height of the yardstick is to the length of its shadow.
Height of telephone pole / Length of telephone pole's shadow = Height of yardstick / Length of yardstick's shadow
Height of telephone pole / 248 inches = 1 yardstick / 2 feet
To solve for the height of the telephone pole, we can cross-multiply and divide:
Height of telephone pole = (1 yardstick / 2 feet) * 248 inches
= (1 / 2) * 248 inches
= 124 inches
Therefore, the height of the telephone pole is 124 inches, to the nearest inch.
To find the height of the telephone pole, we can set up a proportion using the lengths of their shadows.
Let's convert all the lengths to inches to make the problem more manageable:
- The shadow of the yardstick is 24 in.
- The shadow of the telephone pole is 20 ft 8 in., which converts to (20 * 12) + 8 = 248 in.
Now, let's set up the proportion:
(Height of telephone pole) / 248 = (Height of yardstick) / 24
To solve for the height of the telephone pole, we can cross-multiply and then divide 248 by 24:
(Height of telephone pole) = (Height of yardstick) * (248 / 24)
Given that a yard is 36 inches:
(Height of telephone pole) = (36) * (248 / 24)
Simplifying further:
(Height of telephone pole) = (36) * (10.3333...)
Calculating this:
(Height of telephone pole) ≈ 372.0001...
Rounding this to the nearest inch, the height of the telephone pole is approximately 372 inches.