Derek wants to determine the height of the top of the backboard on the basketball goal at the playground. He places a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 10 inches and the backboard has a shadow of 7.75 feet, then how high is the top of the backboard
To determine the height of the top of the backboard, we can use the concept of similar triangles.
First, we need to convert the units so that they are consistent. Since the ruler's shadow is given in inches and the backboard's shadow is given in feet, we need to convert the 7.75 feet into inches. Since there are 12 inches in a foot, we can multiply 7.75 by 12 to get 93 inches.
Now, we have two similar triangles: the triangle formed by the ruler and its shadow, and the triangle formed by the backboard and its shadow.
Let's represent the height of the backboard (which we want to find) as x. The height of the ruler is 12 inches, and the lengths of the shadows are 10 inches and 93 inches, respectively.
Using the concept of similar triangles, we can set up the following proportion:
(Height of the backboard)/(Length of the backboard's shadow) = (Height of the ruler)/(Length of the ruler's shadow)
x/93 inches = 12 inches/10 inches
Now we can solve for x by cross-multiplying:
10x = 93 * 12
10x = 1116
Dividing both sides by 10, we get:
x = 1116/10
x = 111.6 inches
Therefore, the height of the top of the backboard is 111.6 inches.
12/10 = x/7.75
Cross multiply and solve for x.