# How do you find the remaining sides of a #45^circ-45^circ-90^circ# triangle if the longest sides are each #5sqrt2#?

In a 45-45-90 triangle, the longest side has to be the hypotenuse. The other two sides would be the same (in this case, 5).

Each of the legs are 5 units long

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In a 45°-45°-90° triangle, the ratio of the lengths of the sides is (1:1:\sqrt{2}). If the longest sides (hypotenuse) are each (5\sqrt{2}), then the shorter sides (legs) are equal and can be found by dividing the length of the hypotenuse by (\sqrt{2}).

So, if the longest sides are each (5\sqrt{2}), then each shorter side (leg) is:

[ \frac{5\sqrt{2}}{\sqrt{2}} = 5 ]

Therefore, the lengths of the shorter sides (legs) are (5) units each.

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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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