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Question

If in any triangle the angles be to one onother as 1:2:3, prove that the corresponding sides are as 1:3:2,

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Solution

Let A,2A,3A be the angles
Then A+2A+3A=180o or A=30o
The angle are 30o, 60o and 90o.
If a,b,c denote the sides opposite to these angles,
then
asin30o=bsin60o=csin90o
a:b:c=sin30o:sin60o:sin90o
=1/2:3/2:1=1:3:2

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