# Angles by cosine law

Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).

Result

A =  21.787 °
B =  38.213 °
C =  120 °

#### Solution:

$a=3 \ \\ b=5 \ \\ c=7 \ \\ A_{1}=\arccos((b^2+c^2-a^2)/(2 \cdot \ b \cdot \ c))=\arccos((5^2+7^2-3^2)/(2 \cdot \ 5 \cdot \ 7)) \doteq 0.3803 \ \\ A=A_{1} \rightarrow \ ^\circ =A_{1} \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =21.78679 \ \ ^\circ =21.787 ^\circ =21^\circ 47'12"$

Try calculation via our triangle calculator.

$B_{1}=\arccos((a^2+c^2-b^2)/(2 \cdot \ a \cdot \ c))=\arccos((3^2+7^2-5^2)/(2 \cdot \ 3 \cdot \ 7)) \doteq 0.6669 \ \\ B=B_{1} \rightarrow \ ^\circ =B_{1} \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =38.21321 \ \ ^\circ =38.213 ^\circ =38^\circ 12'48"$
$C=180-A-B=180-21.7868-38.2132=120=120 ^\circ$

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Tips to related online calculators
Cosine rule uses trigonometric SAS triangle calculator.
Pythagorean theorem is the base for the right triangle calculator.

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