In a right triangle, is the side opposite the right angle the shortest side?

Answer 1

No. It is the longest side. It can be shown by using the Sines Theorem.

We will show that the side opposite to the right angle is the longest side in a right triangle.

According to the Sine Theorem for every triangle we have:

#a/sinA=b/sinB=c/sinC#
Let's assume, that angle #C# is right. So the last fraction is equal to #c# (the denominator becomes #1#), so we can write that:
#a/sinA=c# and #b/sinB=c#.
So we can calculate #a# and #b# in terms of side #c#
#a=c*sinA# and #b=c*sinB#
#A# and #B# are accute angles, so we can write, that #sinA in (0;1)# and #sinB in (0;1)#, so if #sinA<1# then #a=c*sinA < c#
In the same way we can show that #b=c*sinB < c#, so finally both #a# and #b# are smaller than #c# which concludes the proof.
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Answer 2

Yes, in a right triangle, the side opposite the right angle, known as the hypotenuse, is the longest side. The side adjacent to the right angle, called the adjacent side, and the side opposite the acute angle, called the opposite side, are typically shorter than the hypotenuse.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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