Myk is 5 feet and 2 inches tall, and their shadow is 84 inches tall. The flagpole next to them has a shadow that is 31 feet long. Myk uses similar triangles to find the height of the flagpole. Can you calculate the height of the flagpole to the nearest foot?(1 point)
Responses
23 inches
23 inches
23 feet
23 feet
17 feet
17 feet
374 feet
To calculate the height of the flagpole, we can use the concept of similar triangles.
Let's start by converting Myk's height to inches. Since there are 12 inches in a foot, we have:
5 feet = 5 * 12 inches = 60 inches
2 inches
Total height = 60 inches + 2 inches = 62 inches
Now, let's set up a proportion using the ratios of the corresponding sides of the two triangles:
Myk's height / Myk's shadow = Flagpole's height / Flagpole's shadow
Plugging in the given values, we get:
62 inches / 84 inches = h / 31 feet
To find the height of the flagpole (h), we can cross multiply and solve for h:
62 inches * 31 feet = 84 inches * h
1922 inches-feet = 84 inches * h
Now, let's divide both sides by 84 inches:
h = (1922 inches-feet) / (84 inches)
Since we're looking for the height in feet, let's convert inches-feet to just feet by dividing by 12:
h = (1922 inches-feet) / (84 inches) = 1922/84 = 22.88 feet
Rounded to the nearest foot, we get 23 feet. Therefore, the height of the flagpole to the nearest foot is 23 feet.