2. a flagpole casts a shadow that is 50 feet long. at the same time, a woman standing nearby who is five feet six inches tall casts a shadow 4 feet long. how tall is the flagpole? a. draw a picture to , if needed. b. show your work to receive full credit!

Part A. 

See the attached image for the drawing.

The points shown are
A = edge of shadow
B = person's feet
C = base of flagpole
D = top of flagpole
E = person's head

The ray of light travels from D, through E and ends at point A on the ground. The ground is line AC, which is where the shadow lays. The pole is line segment CD. The person is line segment EB.

The 66 is the woman's height in inches only (6 ft, 5 in = 6 ft + 5 in = 6*12+5 = 66 inches)
The 600 inches comes from the fact that 50 ft = 600 inches (50*12 = 600)
The 48 is due to the fact that 4 ft = 48 inches
The 552 is the difference of 600 and 48, so 600-48 = 552

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Part B

In the drawing for part A, we have two triangles. They are similar triangles (due to the AA similarity theorem), so we can set up the following proportion
x/66 = 600/48

Cross multiply to solve for x
x/66 = 600/48
48*x = 66*600
48*x = 39600
x = 39600/48
x = 825

The height of the flagpole is 825 inches tall
To convert this to feet, divide by 12
825/12 = 68.75

So 825 inches = 68.75 ft

To convert to ft & inches combined, we multiply the decimal portion 0.75 by 12 to get 0.75*12 = 9

So the flagpole is 68 ft, 9 inches tall
(there are at least 3 different ways to express the same height)