Calculate 2

Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm

Result

A =  129.758 °

Solution:

a=5.2 cm b=3.6 cm c=2.1 cm  a>b>c=>A>B>C  a2=b2+c22bccosA  A1=arccos(b2+c2a22 b c)=arccos(3.62+2.125.222 3.6 2.1)2.2647 A=A1 =A1 180π  =129.75829  =129.758=1294530"a=5.2 \ \text{cm} \ \\ b=3.6 \ \text{cm} \ \\ c=2.1 \ \text{cm} \ \\ \ \\ a>b>c=> A>B>C \ \\ \ \\ a^2=b^2+c^2 - 2bc \cos A \ \\ \ \\ A_{1}=\arccos(\dfrac{ b^2+c^2-a^2 }{ 2 \cdot \ b \cdot \ c } )=\arccos(\dfrac{ 3.6^2+2.1^2-5.2^2 }{ 2 \cdot \ 3.6 \cdot \ 2.1 } ) \doteq 2.2647 \ \\ A=A_{1} \rightarrow \ ^\circ =A_{1} \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =129.75829 \ \ ^\circ =129.758 ^\circ =129^\circ 45'30"

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