Jessica E.

asked • 03/20/20

The length of the longer leg of a 30°-60°-90° triangle is 12 cm. What is the length of the hypotenuse? What is the length of the shorter leg?

The length of the longer leg of a 30°-60°-90° triangle is 12 cm. What is the length of the hypotenuse? What is the length of the shorter leg?

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Aaron M. answered • 03/20/20

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In a 30-60-90 triangle, the ratio of the sides is always 1-√3-2. Thus, the side that we're given is the √3 in this ratio so we can solve this by a ratio. 1/√3=x/12 and this makes 12/√3x or x=12/√3 cm for the shorter leg. Since the hypotenuse is twice that length, it would be 24/√3 cm.

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Aaron M.

Yes, I realize that I did not rationalize these. If you wish to do so, multiply by √3/√3 as that's the same as multiplying by 1 so nothing changes.
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03/20/20

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