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 receive full credit for the problem

Answer 1

Let x be the height of tree B.
Since tree A is 12 ft tall and casts a shadow that is 216 inches long, we can set up the proportion 12 ft / 216 in = x ft / (216 in - 1.5 ft).
Converting 12 ft to inches, we get 12 ft * 12 in/ft = 144 in.
Combining like terms in the denominator, we get 216 in - 1.5 ft * 12 in/ft = 216 in - 18 in = 198 in.
Cross-multiplying the proportion, we get 12 ft * 198 in = 216 in * x ft.
Simplifying the left side, we get 2376 in = 216 in * x ft.
Dividing both sides by 216 in, we get 2376 in / 216 in = x ft.
Simplifying the left side, we get 11 ft = x ft.
Therefore, tree B is 11 ft tall. Answer: \boxed{11}.