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Given the lengths of the sides of a triangle are in the ratio of 3:8:6, what is the degree measure of the largest angle? Please explain.

 Sep 15, 2019
 #1
avatar+104911 
+2

We can use the Law of Cosines to solve this   [although there may be other ways, too]

 

We have that

 

8^2  =  3^2 + 6^2  - 2 (3)(6) cos  A        rearrange  as

 

[8^2  - 3^2 -6^2] / [ -2 (3) (6) ]  = cos A     simplify

 

[ 19] / [ -36]  = cos A

 

-19/36  = cos A        and we can find the angle A  with the cosine inverse  (arccos)

 

arccos ( -19/36)  = A  ≈  121.86°

 

P.S.  - this angle is obtuse  ( > 90°)....and a triangle may only have one angle > 90°...so...we know it's the largest

 

 

cool cool cool

 Sep 15, 2019
 #2
avatar+196 
+2

Thank you for your quick answer!!

hellospeedmind  Sep 15, 2019
 #3
avatar+104911 
0

OK, man  !!!

 

 

cool cool cool

CPhill  Sep 15, 2019

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