SOLUTION: THe ratio of the angles of a triangle is 1:2:3. If the shortest side of the triangle has length 5 square root of 3. what is the length of the next larger side?

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Whoops, originally thought the sides were 1:2:3, not the angles.

If the angles are in the ratio 1:2:3, the triangle is a 30-60-90 triangle (by using x + 2x + 3x = 180 --> x = 30). The shortest side has length so the next larger side is the shortest side times (since the next larger side cannot be the hypotenuse). So the next larger side is 15.

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The shortest side is opposite the smallest angle
the ratios of the sides of a 30-60-90 triangle are
::



The next longer side is 15 units long
check:
sides are:
opposite 30:
opposite 60:
opposite 90:



OK