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.
First, we need to convert the height of Tree A and the length of its shadow to the same unit of measurement. Since Tree A's height is given in feet and the length of its shadow is given in inches, we need to convert feet to inches.
Tree A's height: 12 ft = 12 * 12 = 144 inches
Next, we can set up a proportion using the height and shadow length of Tree A and Tree B.
Let's say the height of Tree B is x feet.
Height ratio: Tree A's height / Tree B's height = Shadow length ratio: Tree A's shadow length / (Tree B's shadow length - 1.5 ft)
144 / x = 216 / (x * 12 - 1.5 * 12)
Now, we can cross multiply and solve for x.
144 * (x * 12 - 1.5 * 12) = 216 * x
1728x - 216 = 216x
1728x - 216x = 216
1512x = 216
x = 216 / 1512
x = 0.14285714285714285 ft
Since 1 foot = 12 inches, we can convert the height of Tree B from feet to inches.
Height of Tree B: 0.14285714285714285 ft * 12 = 1.7142857142857144 inches
Therefore, Tree B is approximately 1.71 inches tall.