a burro is standing near a cactus. the burro is 59 in. all. his shadow is 4 ft long. the shadow of the cactus is 7 ft long. estimate the height of the cactus
My estimate is 8 1/2 feet. What is your estimate?
9 ft
My estimate is 8 or 9, give or take a few
To estimate the height of the cactus, we can use the concept of similar triangles. The height of the burro can be considered as one side of a triangle, and the length of its shadow can be considered as the corresponding side of a similar triangle.
First, let's convert the measurements to the same unit. The burro's height is 59 inches, and its shadow is 4 feet long. Since there are 12 inches in a foot, the burro's shadow is 4 * 12 = 48 inches long.
Next, we need to compare the lengths of the shadows to estimate the height of the cactus. The burro's shadow is 48 inches long, while the shadow of the cactus is 7 feet long. Converting this to inches, the cactus shadow is 7 * 12 = 84 inches long.
Now, we can set up a proportion using the side lengths of the similar triangles:
Height of burro / Length of burro's shadow = Height of cactus / Length of cactus shadow
Substituting the values we found:
59 inches / 48 inches = Height of cactus / 84 inches
To solve for the height of the cactus, we can cross-multiply and then divide:
( 59 inches * 84 inches ) / 48 inches = Height of cactus
Calculating this, the estimated height of the cactus is approximately 103.5 inches.