Sides ratio and angles

In triangle ABC, you know the ratio of side lengths a:b:c=3:4:6. Calculate the angle sizes of triangle ABC.

Final Answer:

α =  26.3843 °
β =  36.3361 °
γ =  117.2796 °

Step-by-step explanation:

a:b:c=3:4:6 a:b:c=3x:4x:6x  a=3x b=4x c = 6x  a2 = b2+c2  2 b c cos α  α = arccos(2 b cb2+c2a2)  α=π180°arccos(2 4 642+6232)=26.3843=26°234"
β = arccos(2 a ca2+c2b2)  β=π180°arccos(2 3 632+6242)=36.3361=36°2010"
γ = arccos(2 a ba2+b2c2)  γ=π180°arccos(2 3 432+4262)117.2796   Verifying Solution:   s=α+β+γ=26.3843+36.3361+117.2796=180 



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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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