Question 132347: I have a word problem I'd like to check please. On a baseball diamond the bases are 90 ft apart. What is the distance from home plate to second base in a straight line?
I tried using the pythagorean formula and squared both sides of 90 and added them together to get 16200. The square root from that would be 127.279, and that is what I think the distance would be. Can you tell me if I'm not right & point me in the right direction?
Found 2 solutions by checkley71, solver91311:
Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website! YOU HAVE A RIGHT TRIANGLE WITH EQUAL SIDES (80FEET) & ARE SOLVING FOR THE HYPOTENUSE.
90^2+90^2=X^2
8100+8100=X^2
16,200=X^2
X=SQRT16,200
X=127.279 ANSWER.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website! Your answer is a very close approximation of the straight line distance from home plate to second base, and probably significantly more accurate than the measurement of the distance from home plate to first base or from first base to second base.
127.27922061357855439215198517887 is an even more precise approximation, yet it is still only an approximation.
You arrived at calculating the square root of 16200. If you do a prime factorization of 16200, you will get:
2 X 2 X 2 X 3 X 3 X 3 X 3 X 5 X 5 which can be combined into the following factors:
2 X 81 X 100. Now,  and  is the simplest form EXACT answer to the question.
On the other hand, you really shouldn't give an exact answer to this problem because the input data is a measurement, and no measurement is exact. Furthermore, the result of a calculation based on a measurement should never be expressed with greater precision than the precision of the least precise given measurement. In this case, since the measurement given was to the nearest foot, i.e. 90 feet, the answer should be no more precise than that, i.e. your answer should be 127 feet. Your three decimal place answer would only be appropriate if the given measurement had been 90.000 feet.
What's the difference between saying 90 feet and 90.000 feet you ask? A whole world of difference. Saying the bases are 90 feet apart only guarantees that the exact distance is somewhere in the interval  , or in ordinary language, "the bases are 90 feet apart, give or take 6 inches", whereas saying the measurement is 90.000 means the exact distance is confined to the interval  .
So you have choices.
If your assignment wants the exact answer based on the assumption that the bases are exactly 90 feet apart, then the answer is .
If your assignment wants an appropriate approximation, then the answer is 127 feet, but you could give 127.279 as an answer at the risk of being inappropriately precise.
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