Three angles

Find all missing angle values using the Law of Cosines, given all three sides:

a = 12, b = 13, and c = 20

Final Answer:

α =  35.1838 °
β =  38.6248 °
γ =  106.1914 °

Step-by-step explanation:

a=12 b=13 c=20  a2 = b2+c2 − 2 b c cos α  k1​=2⋅ b⋅ cb2+c2−a2​=2⋅ 13⋅ 20132+202−122​=10485​≐0.8173  α=π180°​⋅arccos(k1​)=π180°​⋅arccos0.8173=35.1838∘=35°11′2"
b2 = a2+c2 − 2 a c cos β  k2​=2⋅ a⋅ ca2+c2−b2​=2⋅ 12⋅ 20122+202−132​=3225​≐0.7813  β=π180°​⋅arccos(k2​)=π180°​⋅arccos0.7813=38.6248∘=38°37′29"
c2 = a2+b2 − 2 ab cos γ  k3​=2⋅ a⋅ ba2+b2−c2​=2⋅ 12⋅ 13122+132−202​=−10429​≐−0.2788  γ=π180°​⋅arccos(k3​)=π180°​⋅arccos(−0.2788)=106.1914∘=106°11′29"

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planimetricsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem

 
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