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).

Final 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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Tips for related online calculators
The Pythagorean theorem is the base for the right triangle calculator.
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

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planimetricsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem

 
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