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hypotenuse = √2 x leg

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hypotenuse = 2 x shorter leg
longer leg = √3 x shorter leg

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In a 30 60 90 triangle, the length of the shorter leg. The length of the longer leg is √3 times the length of the shorter leg.

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The hypotenuse faces the the larger angle (90 degrees) as the congruent legs face the 45 degree angles.

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If each leg has length x and the hypotenuse has length y, you can solve for y in terms of x

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If each leg has length x and the hypotenuse has length y, you can solve for y in terms of x

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A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. - Wikipedia

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A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. - Wikipedia

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In a  45 45 90 triangle, both legs are congruent and the length of the hypotenuse is √2 times the length of a leg.