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 A1=arccos((b2+c2a2)/(2 b c))=arccos((52+7232)/(2 5 7))0.3803 A=A1 =A1 180π  =21.7867892983  =21.787=214712"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 = 21.7867892983 \ \ ^\circ = 21.787 ^\circ = 21^\circ 47'12"

Try calculation via our triangle calculator.

B1=arccos((a2+c2b2)/(2 a c))=arccos((32+7252)/(2 3 7))0.6669 B=B1 =B1 180π  =38.2132107018  =38.213=381248"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 = 38.2132107018 \ \ ^\circ = 38.213 ^\circ = 38^\circ 12'48"
C=180AB=18021.786838.2132=120=120C = 180-A-B = 180-21.7868-38.2132 = 120 = 120 ^\circ







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Following knowledge from mathematics are needed to solve this word math problem:

Cosine rule uses trigonometric SAS triangle calculator. See also our trigonometric triangle calculator. Pythagorean theorem is the base for the right triangle calculator.