SOLUTION: given a triangle with sides 4, 5, 6. find the EXACT values of the angles to show that one angle is EXACTLY twice the other (no estimations).

Question 275040: given a triangle with sides 4, 5, 6. find the EXACT values of the angles to show that one angle is EXACTLY twice the other (no estimations).
Answer by kensson(21) (Show Source): You can put this solution on YOUR website!
Interesting!
The cosine rule is:
Or, rearranging,
So the cosine of the angle opposite the 4 side is = 45/60 = 3/4.
Opposite the 5: = 27/48 = 9/16.
Opposite the 6: = 5/40 = 1/8.
So the smallest angle is arccos(3/4), the middle angle is arccos(9/16) and the biggest angle arccos(1/8).
Now, . For the smallest angle:

So the largest angle is twice the size of the smallest one.

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