Question

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 8.5 feet, then how high is the top of the backboard?

Answer 1

Answer:

10.2 feet.

Step-by-step explanation:

We have been given that Derek 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. We are asked t find the height of the backboard, if the backboard has a shadow of 8.5 feet.

We will use proportions to solve our given problem as ratio between sides ruler will be equal to ratio of sides of background.

$\frac{\text{Actual height of ruler}}{\text{Shadow of ruler}}=\frac{\text{Actual height of backboard}}{\text{Shadow of backboard}}$

$\frac{12}{10}=\frac{\text{Actual height of backboard}}{8.5}$

$\frac{12}{10}*8.5=\frac{\text{Actual height of backboard}}{8.5}*8.5$

$1.2*8.5=\text{Actual height of backboard}$

$10.2=\text{Actual height of backboard}$

Therefore, the actual height of the back-board is 10.2 feet.

Answer 2

Answer:

Step-by-step explanation:

Since the backboard and the ruler are both vertical and the sun is at the same position in the sky, the triangle made by the backboard and its shadow is similar to the triangle made by the ruler and its shadow.

The ratio of the corresponding sides of the triangles are equal and the height of the backboard can be determined by solving the following proportion.

Therefore, the top of the backboard is 7.64 feet high.