Largest angle of the triangle

Calculate the largest angle of the triangle whose sides have the sizes:
2a, 3/2a, 3a

Final Answer:

γ =  117.2796 °

Step-by-step explanation:

x=1 a=2⋅ x=2⋅ 1=2 b=3/2⋅ x=3/2⋅ 1=23​=1.5 c=3⋅ x=3⋅ 1=3  c>a>b => γ>α>β  c2 = a2+b2 − 2⋅ a⋅ b⋅ cos γ  C=arccos(2⋅ a⋅ ba2+b2−c2​)=arccos(2⋅ 2⋅ 1.522+1.52−32​)≐2.0469 rad  γ=C→  °=C⋅ π180​   °=2.0469⋅ π180​   °=117.28  °=117.2796∘=117°16′47"

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You need to know the following knowledge to solve this word math problem:

algebraplanimetrybasic operations and conceptsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem

 
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