SOLUTION: Three numbers A, B, C are in ratio a: b: c, if the following proportion is true: A/a=B/b=C/c. If the angles of a triangle are in ratio 3: 4: 5, find the ratio of the corresponding

Question 1198385: Three numbers A, B, C are in ratio a: b: c, if the following proportion is true:
A/a=B/b=C/c. If the angles of a triangle are in ratio 3: 4: 5, find the ratio of the corresponding sides
Answer by ikleyn(52800) (Show Source): You can put this solution on YOUR website!
.
Three numbers A, B, C are in ratio a: b: c, if the following proportion is true:
A/a=B/b=C/c. If the angles of a triangle are in ratio 3: 4: 5,
find the ratio of the corresponding sides
~~~~~~~~~~~~~~~~~~

If the angles of the triangle are in ratio A:B:C = 3:4:5, it means that
A = 3x, B = 4x, C = 5x,  where x is the common measure.


Then 3x + 4x + 5x = = 180°,  or  12x = 180°,  which implies  x = 180°/12 = 15°.


Hence, A = 45°,  B = 60°,  C = 75°.


Due to the sine law, it implies

     =  = .


Thus the ratio of the corresponding sides is  

    a:b:c = sin(45°) : sin(60°) : sin(75°) =  :  :  = 

                                           =  :  :  = 1.414 : 1.732 : 1.932 (rounded).   ANSWER

Solved.

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