SOLUTION: Find the indicated measure A building cast a shadow of a 18 feet long.A woman standing near the building is 5 feet 8 inches tall and casts a shadow 4 feet long. What is the heig

Question 118972: Find the indicated measure
A building cast a shadow of a 18 feet long.A woman standing near the building is 5 feet 8 inches tall and casts a shadow 4 feet long. What is the height of the building in feet and inches?
Any help with this equation would be Greatly appreciated.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Assuming that the woman is standing up straight, you have a situation where you have two similar right triangles. The legs of the smaller triangle are the woman's height and the length of her shadow, and the legs of the larger triangle are the building's height and the length of its shadow. We know that the sides of similar triangles are proportional, so we can write:

Now you need to cross-multiply and solve for x, but multiplying feet times feet and inches is a messy calculation. Changing 5 ft 8 inches to 5 and 2/3 feet is messy also. My recommendation is to convert everything to inches, and then convert back to feet and inches when you are done.

5 ft 8 inches = (5 *12) + 8 = 68 inches
4 ft = 4 * 12 = 48 inches, and
18 ft = 18 * 12 = 216 inches.

Now the proportion looks like:
, so

after cross-multiplying, and

after dividing by 48. So the building is 306 inches tall. But we want to know the height of the building in feet and inches. To convert back to feet and inches from inches, just do integer division by 12 where your answer is expressed as a quotient and a remainder. The quotient is the number of feet, and the remainder is the number of inches.

= 25 remainder 6, so the answer is 25 feet 6 inches.

Note that this answer makes sense. 5'8" is nearly 6'. 6' is one and a half times 4 feet, so the woman is a little less than one and a half times taller than her shadow is long. One and a half times the building's 18 ft shadow is 27 feet, and that is a little bit more than the 25'6' answer that we got.

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