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# Q: If the hypotenuse of a right triangle is 20, what is the

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Intern
Joined: 22 Jan 2005
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Q: If the hypotenuse of a right triangle is 20, what is the [#permalink]

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22 Jan 2005, 13:16
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Q: If the hypotenuse of a right triangle is 20, what is the length of the leg opposite the 45 degree angle?

I believe this is a 45, 45, 90 triangle. If the hyp = 20 = x*sq. rt. of 2.

So, 20 = x*sq rt of 2

The answer is 10 which means x = 10. But that would make
the hyp = 10*sq rt of 2

Any thoughts?

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Director
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22 Jan 2005, 13:35
I think the side opposite the 45 degree angle is 20/sq rt 2

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Director
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22 Jan 2005, 13:43
think of it like this for any 45 45 90 the sides are in the ratio

1:1: root 2 side side hyp

so if hyp = 20 the other 2 sides will be 10 root 2

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Director
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22 Jan 2005, 13:45
x^2 + x^2 = 20^2

This implies x^2 = 200
or x = SQRT(200) = 10*(SQRT(2))

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Intern
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22 Jan 2005, 14:22
the pythagorean theorem (applies in ANY right triangle) states that the square of the hypothenuse (c) equals the sum of the squares of the other two sides (a, b), id est: c^2=a^2+b^2. In this case, a=b. So 2a^2=20^2 -> a=SQRT (200)

f.

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Director
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22 Jan 2005, 14:55
oops, what was i thinking?

Ans should be sq rt 200 = 10sq rt 2

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SVP
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22 Jan 2005, 22:15
2a^2=400
a=10sqrt(2)

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22 Jan 2005, 22:15
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# Q: If the hypotenuse of a right triangle is 20, what is the

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