Question 139374: Tell whether a triangle with the sides of the given lengths is 45°-45° -90°, 30° -60° -90° or neither.
11, 22, 19.1
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Well, that sort of depends on how precise you want to be. A triangle with sides of 11, 22, and 19.1 is very, very close to a 30°-60°-90° triangle. That is because a 30°-60°-90° triangle with a hypotenuse of 22 has sides of 11 and  . 19.1 is pretty close to but not exactly, and in fact the only way to express the length of the long leg of the given triangle exactly is to say . That is because  is an irrational number and there is no exact decimal equivalent because there are no two integers p and q such that  .
So, a mathematician must answer this question: Neither, because  . Presuming that the triangle is a right triangle having sides of 11, 22, and 19.1, it would be approximately a 29.752°, 60.248°, 90° triangle.
A landscape architect laying out a triangular flower bed in your back yard would say: 30°-60°-90° because 19.1 is a precise enough measurement for the purpose.
On the other hand, a rocket scientist planning an earth to the moon trajectory would say Neither, because in this case 19.1 isn't nearly close enough to the true value of for this purpose. That one-quarter of a degree error in angular measure here on earth means missing the moon by over 1000 miles at the end of the 240,000 mile trip.
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