SOLUTION: In the given 30-60-90 triangle, one leg is 10 mm, find the measure of the other leg and the hypotenuse.

Algebra ->  Triangles -> SOLUTION: In the given 30-60-90 triangle, one leg is 10 mm, find the measure of the other leg and the hypotenuse.      Log On


   

Question 593946: In the given 30-60-90 triangle, one leg is 10 mm, find the measure of the other leg and the hypotenuse.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is this "one leg" the shorter leg? Or is this the longer leg?

If it's the shorter leg, then the hypotenuse is twice that at 2*10 = 20 mm

Again, if it's the shorter leg, then the longer leg is 10%2Asqrt%283%29 mm


In general, if x is the shorter leg in a 30-60-90 triangle, then 2x is the hypotenuse and x%2Asqrt%283%29 is the longer leg.

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OR

If the "one leg" is the longer leg, then the shorter leg 'x' is 10+=+x%2Asqrt%283%29 ----> x+=+10%2Fsqrt%283%29+=+%2810%2Asqrt%283%29%29%2F3


So the shorter leg 'x' is x+=+%2810%2Asqrt%283%29%29%2F3 mm long


and the hypotenuse 'h' is h+=+2x+=+2%28%2810%2Asqrt%283%29%29%2F3%29+=+%2820%2Asqrt%283%29%29%2F3


So the hypotenuse 'h' is h+=+%2820%2Asqrt%283%29%29%2F3 mm long