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3 years ago

Which angle measures create a triangle with three different side lengths?

Mathematics

1 answer:

dedylja [7]3 years ago

3 0

Answer:

Step-by-step explanation:

For 3 different side lengths, you need 3 different angles. That eliminates A, B and D.

A: In the case of A, The angles do not add up to 180 so this is not possible. Even if it was, the angles are all the same and the side lengths would be as well.

B: Two angles are the same, therefore, 2 sides will be the same, even though the two sides added together will be larger than the side opposite.

D: Two angles are the same. The angles add to 180. The triangle will have 2 equal sides.

C: Answer. The three given angles add to 180. They are different. Unless the side opposite 93 exceeds the length of the other 2 sides, this forms a triangle with 3 different sides. Using other methods to calculate the answer the other 2 sides do exceed the the base length so everything is fine.

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• Let n be even. Then we can write n = 2k for some integer k ≥ 0. Now,

[n/2] = [k] = k

while

[-n/2] = [-k] = -k

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• Let n be odd. Then n = 2k + 1 for some integer k ≥ 0. Every odd integer occurs between two even integers, so that

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or equivalently,

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Similarly, if we negative the previous inequality, we have

-k > -n/2 > -(k + 1), or -k - 1 < -n/2 < -k

which means [-n/2] = -k - 1.

So we make the same conclusion,

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