SOLUTION: What are the values of the side lengths of a triangle with 30 degrees, 60 degrees, 90 degree angles and a short leg =13

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Question 1089034: What are the values of the side lengths of a triangle with 30 degrees, 60 degrees, 90 degree angles and a short leg =13
Found 2 solutions by math_helper, MathLover1:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

Side opposite the 60 degree angle: +13%2Asqrt%283%29+
Side opposite the 90 degree angle: +26+
——
Workout:
Use Law of Sines and solve for unknowns (a=side opposite 60, h=side opposite 90):
+sin%2830%29%2F13+=+sin%2860%29%2Fa+=+sin%2890%29%2Fh+
Check: +a%5E2+%2B+13%5E2+=+%2813sqrt%283%29%29%5E2+%2B+169+=+507+%2B+169+=+676+=+26%5E2+=+h%5E2+ (ok)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
All 30-60-90-degree triangles have sides with the same basic ratio.

In any 30-60-90 triangle, you see the following:
1. The shortest leg is across from the 30-degree angle.
2. The length of the hypotenuse is always+two times the length of the shortest leg.
3. You can find the long leg by multiplying the short leg by the square sqrt%283%29.

if a short_leg+=13, than
=>the hypotenuse=2%2A13=26 and
the long leg is 13sqrt%283%29