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

The angles are 35 degrees, 55 degrees and 90 degrees.

We know that a/Sin A = b/Sin B = C/sin C = k say

a= k sin 35 degrees

b= k sin 55 degrees

c = k sin 90 degrees

a= k(0.5735)

b= k(0.8191)

c= k

a+b+c = k(2.3928) =35

k = 35/2.3928 =14.6277

a=14.6277* 0.5735 =8.39

b= 14.6277*0.8191 =11.98

c= 14.6277*1 = 14.63

The sides are 8.39, 11.98,14.63

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