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

Answer 1

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).

The ratio of the sides of an isosceles right triangle (45-45-90) is #1:1:sqrt2# (leg:leg:hypotenuse). The hypotenuse is found by multiplying the length of the leg by #sqrt2#.

To find the length of a leg from the hypotenuse, divide by #sqrt2#

#(5sqrt2)/sqrt2=5#

Each of the legs are 5 units long

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Answer 2

Dylan Arnold

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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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.