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What is the height of a flagpole if a person 5 feet tall casts a 10 foot shadow at the same time that the flagpole casts a 40 foot shadow?
The flag pole would be 20 feet. (You can see that the shadows are twice as long.) At a given time of the day, the length of a shadow cast by any object will have the same relationship to its actual height as all other objects. Here the ratio is 5/10 = x/40 and multiplying both sides by 40, 20 = x.
A 3 foot pole casts a 6 foot shadow A 4 foot pole casts an 8 foot shadow Use a linear equation to predict the length of a shadow cast by a 6 foot pole?
Shadow lengths are proportional to the heights of objects casting the shadows. Therefore, calling the shadow length l, the height h, and the proportionality constant k, l = kh. (The intercept is 0 because an object with no height casts no shadow.) Therefore, in this instance k = l/h = 6/3 or 8/4 = 2. then l(6) = 2 X 6 = 12 feet.
The shadow cast by a house is 55 feet long.At the same time a flagpole that is 15 feet tall casts a 25 foot long shadow.How tall is the house?
25
If a 30 foot flagpole casts a 12 foot shadow how tall is a mailbox casting a 18 inch shadow?
To solve this problem, we can set up a proportion using the similar triangles formed by the flagpole and its shadow, and the mailbox and its shadow. The height of the flagpole to its shadow is 30 feet to 12 feet, which simplifies to 5:2. Using this ratio, we can determine the height of the mailbox by setting up the proportion 5/2 = x/1.5 (converting 18 inches to feet). Solving for x, the height of the mailbox would be 3.75 feet.
How high is a tree that casts a 21 foot shadow at the same time a 6.5 foot man cast a 5 foot shadow?
27.3 feet
