The figure shows the shadows created by the sun when Cindy stands near the flagpole.
Cindy on the left, she’s ACTUALLY 5 ft and her SHADOW is 4 ft. The flagpole is on the right, we don’t know what the ACTUAL height is but the SHADOW is 10 ft.
What is the closest to the height of the flagpole?
A. 2 ft 6 in.
B. 8 ft
C. 12 ft
D. 12 ft 6 in.
Eliminating A and C, it has to be either B or D. I don't know, please help, you guys are so nice! :)
solve the simple proportion
5/4 = h/10
I went w c
To find the height of the flagpole, we can use the concept of similar triangles. Similar triangles have proportional sides.
First, let's compare Cindy and her shadow. We have her actual height of 5 ft and her shadow length of 4 ft. Since both Cindy and her shadow are standing on the same ground, we can conclude that the height and the shadow form a right angle. Therefore, we have a right triangle.
Using the Pythagorean theorem (a^2 + b^2 = c^2), we can find the hypotenuse (the length of the shadow):
4^2 + 5^2 = c^2
16 + 25 = c^2
41 = c^2
Taking the square root of both sides, we find:
c = √41
c ≈ 6.4 ft
Now, let's compare the flagpole and its shadow. We have the shadow length of the flagpole as 10 ft. Similar to Cindy's case, we can conclude that the height of the flagpole and its shadow form a right triangle.
Using the same concept, we can find the height of the flagpole as follows:
h/10 = 5/4
Cross-multiplying, we have:
4h = 50
h = 50/4
h = 12.5 ft
Since the closest option is D (12 ft 6 in), that is the height that is closest to the flagpole's actual height.