SOLUTION: Find the lengths of all three sides of a right triangle that has perimeter 26 and has a 35 degree angle.

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Question 922265: Find the lengths of all three sides of a right triangle that has perimeter 26 and has a 35 degree angle.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= length of the hypotenuse (in the same units used to measure the perimeter).
Then, the legs of that right triangle measure
x%2Asin%2835%5Eo%29=about+0.5736x for the shortest leg, the one opposite the 35%5Eo angle, and
x%2Acos%2835%5Eo%29=about+0.8192x for the longest leg, the one adjacent to the 35%5Eo angle.
Those are not exact values because I am using approximate values for sine and cosine.
The perimeter is (approximately)
x%2B0.5736x%2B0.8192x , and we solve for approximate length the equation
x%2B0.5736x%2B0.8192x=26
2.3928x=26
x=26%2F2.3928
highlight%28x=10.866%29 (rounded) is the length of the hypotenuse
0.5736%2A10.866=highlight%286.233%29 (rounded) is the length of the short leg, and
0.8192%2A10.866=highlight%288.901%29 (rounded) is the length of the long leg.