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 answer:

α =  21.7868 °
β =  38.2132 °
γ =  120 °

Step-by-step explanation:

a=3 b=5 c=7  a2 = b2+c2 − 2⋅ bc cos α A=arccos((b2+c2−a2)/(2⋅ b⋅ c))=arccos((52+72−32)/(2⋅ 5⋅ 7))≐0.3803 rad  α=A→  °=A⋅ π180​   °=0.3803⋅ π180​   °=21.787  °=21.7868∘=21°47′12"
b2 = a2+c2 − 2 ac cos β B=arccos((a2+c2−b2)/(2⋅ a⋅ c))=arccos((32+72−52)/(2⋅ 3⋅ 7))≐0.6669 rad β=B→  °=B⋅ π180​   °=0.6669⋅ π180​   °=38.213  °=38.2132∘=38°12′48"
γ=180−α−β=180−21.7868−38.2132=120∘

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