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# 45-45-90 triangle/ square roots and some trigonometry

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So there's this 45-45-90 triangle, and the hypotenuse is 5 sqrt 26. I know that the lengths of the other two sides are half of that, but I don't really know how to calculate that. (And the answer has to be in square root/radical form....not like decimals and stuff) Can someone help me out?

Jun 6, 2021

#1
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Just to be clear, you want to know what the legs are, right?

If so, then if the hypotenuse is a sqrt 2, then the legs are both a.

in this case, the hypotenuse is 5 sqrt 26. so , the legs are 5 sqrt 13

If I'm wrong, please correct me.

JP

Jun 6, 2021
#2
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Yes, that's exactly what I was looking for! Thank you.

But the number being multiplied by the square root stays the same (in this case 5)? and then actual numbers inside the square root gets divided by 2. 26/2 = 13. That part makes sense, just not the first part- could you clarify?

Guest Jun 6, 2021
#3
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The formula for a 45-45-90 triangle is: legs are a, hypotenuse is a sqrt 2.

Here is a picture for clarity:

JKP1234567890  Jun 6, 2021
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"So there's this 45-45-90 triangle, and the hypotenuse is 5 sqrt 26. I know that the lengths of the other two sides are half of that."

The length of the legs is not 1/2 of the hypotenuse!!!

Hypotenuse = 5√26 = 25.49509757

Leg(s) = 5√13 = 18.02775638

civonamzuk  Jun 6, 2021
edited by civonamzuk  Jun 6, 2021
edited by civonamzuk  Jun 6, 2021