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).

Correct result:

A =  21.7868 °
B =  38.2132 °
C =  120 °

Solution:

a=3 b=5 c=7 A1=arccos⁡((b2+c2−a2)/(2⋅ b⋅ c))=arccos⁡((52+72−32)/(2⋅ 5⋅ 7))≐0.3803 A=A1→∘=A1⋅ 180π∘=0.3803⋅ 180π∘=21.787∘=21.7868∘=21∘47′12"

Try calculation via our triangle calculator.

B1=arccos⁡((a2+c2−b2)/(2⋅ a⋅ c))=arccos⁡((32+72−52)/(2⋅ 3⋅ 7))≐0.6669 B=B1→∘=B1⋅ 180π∘=0.6669⋅ 180π∘=38.213∘=38.2132∘=38∘12′48"
C=180−A−B=180−21.7868−38.2132=120∘

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

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