# Largest angle of the triangle

Calculate the largest angle of the triangle whose sides have the sizes:
2a, 3/2a, 3a

Correct result:

C =  117.28 °

#### Solution:

$x=1 \ \\ a=2 \cdot \ x=2 \cdot \ 1=2 \ \\ b=3/2 \cdot \ x=3/2 \cdot \ 1=\dfrac{ 3 }{ 2 }=1.5 \ \\ c=3 \cdot \ x=3 \cdot \ 1=3 \ \\ \ \\ c>a>b \ \\ c^2=a^2+b^2 - 2 \cdot \ a \cdot \ b \cdot \ \cos(C) \ \\ C=\dfrac{ 180^\circ }{ \pi } \cdot \arccos (\dfrac{ a^2 + b^2 - c^2 }{ 2 \cdot \ a \cdot \ b } )=\dfrac{ 180^\circ }{ \pi } \cdot \arccos (\dfrac{ 2^2 + 1.5^2 - 3^2 }{ 2 \cdot \ 2 \cdot \ 1.5 } )=117.28 ^\circ =117^\circ 16'47"$

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