Question

tree A is 12 ft tall and casts a shadow that is 216 inches long. How tall is tree B if at the same time of day its shadow is 1.5 feet shorter? Make sure to show all work in order to recieve full credit for the promblem?

Answer 1

First, we need to convert the length of tree A's shadow from inches to feet. Since there are 12 inches in a foot, the shadow of tree A is 216/12 = <<216/12=18>>18 feet long.

Next, we need to find the height of tree B. We know that the shadow of tree B is 1.5 feet shorter than tree A's shadow, so the length of tree B's shadow is 18 - 1.5 = <<18-1.5=16.5>>16.5 feet long.

Since the height of a tree is directly proportional to the length of its shadow, we can set up a proportion to solve for the height of tree B. Let x be the height of tree B. We have the proportion:

x / 16.5 = 12 / 18

To solve for x, we can cross-multiply:

18x = 16.5 * 12

18x = 198

Finally, divide both sides by 18 to solve for x:

x = 198 / 18

x = 11

Therefore, the height of tree B is 11 feet.