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?
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.