Question 1198385
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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
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<pre>
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

    {{{a/sin(45^o)}}} = {{{b/sin(60^o)}}} = {{{c/sin(75^o)}}}.


Thus the ratio of the corresponding sides is  

    a:b:c = sin(45°) : sin(60°) : sin(75°) = {{{sqrt(2)/2}}} : {{{sqrt(3)/2}}} : {{{(sqrt(6) + sqrt(2))/4}}} = 

                                           = {{{sqrt(2)}}} : {{{sqrt(3)}}} : {{{(sqrt(6)+sqrt(2))/2}}} = 1.414 : 1.732 : 1.932 (rounded).   <U>ANSWER</U>
</pre>

Solved.