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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Question 388987: 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?
Found 2 solutions by richard1234, josmiceli:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
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 5sqrt%283%29 so the next larger side is the shortest side times sqrt%283%29 (since the next larger side cannot be the hypotenuse). So the next larger side is 15.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
a+%2B+2a+%2B+3a+=+180
6a+=+180
a+=+30
2a+=+60
3a+=+90
The shortest side is opposite the smallest angle
the ratios of the sides of a 30-60-90 triangle are
1:sqrt%283%29:2
1%2Fsqrt%283%29+=+5%2Asqrt%283%29%2Fx
x+=+5%2Asqrt%283%29%2Asqrt%283%29
x+=+15
The next longer side is 15 units long
check:
sides are:
opposite 30:5%2Asqrt%283%29
opposite 60:15
opposite 90:10%2Asqrt%283%29
%285%2Asqrt%283%29%29%5E2+%2B+15%5E2+=+%2810%2Asqrt%283%29%29%5E2
75+%2B+225+=+300
300+=+300
OK