# math

In a triangle ABC a:b:c =4:5:6 then 3A+B=?

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1. Hmmm. If the sides are in the ratio 4:5:6, then the sines of the angles are in the same ratio (law of sines)

So, if sinA = 4x,
sinB = 5x
sinC = 6x

arcsin(4x)+arcsin(5x)+arcsin(6x) = pi
x = √7/16
A = arcsin(4√7/16) = 41.41
B = arcsin(5√7/16) = 55.77
C = arcsin(6√7/16) = 82.82
In degrees, then
3A+B = 180

Wow! Unexpected. Haven't figured out another way to get that, just yet.

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posted by Steve
2. ¦°

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3. saurav Kumar sarwan bazar

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4. 3A+B=2A+180-C
Now sin(2A)=sin(C)=6x
So, 2A=C
3A+B=180

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