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In a 30-60-90 triangle, if the shortest side is 3, what are the lengths of the other two sides (the legs and the hypotenuse)?

A. Legs: 3, Hypotenuse: 6
B. Legs: 3, Hypotenuse: 9
C. Legs: 3, Hypotenuse: 3√3
D. Legs: 3, Hypotenuse: 6√3

User Ncray
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Final answer:

In a 30-60-90 triangle with the shortest side measuring 3, the lengths of the other sides are 3√3 (longer leg) and 6 (hypotenuse), corresponding to answer choice C.

Step-by-step explanation:

In a 30-60-90 triangle, the lengths of the sides are determined by a set of fixed ratios.

If the shortest side, which is opposite the 30-degree angle, is 3, then the length of the side opposite the 60-degree angle (the longer leg) will be 3 times the square root of 3 (3√3), because the ratio between the longer leg and the shorter leg in a 30-60-90 triangle is always √3:1.

The hypotenuse, which is opposite the 90-degree angle, will be twice the length of the shortest side, so in this case it would be 6.

Therefore, the correct answer is C. Legs: 3√3, Hypotenuse: 6.

User Isaac Weingarten
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