SOLUTION: the side of a triangle measure 16 centimeters, 13 centimeters, and 11 centimeters, what are the measures of the angles of the triangle

Question 1001510: the side of a triangle measure 16 centimeters, 13 centimeters, and 11 centimeters, what are the measures of the angles of the triangle

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
In a right triangle the longest side is the hypotenuse,
and if = length of the hypotenuse, with and being the other sides lengths,
(the Pythagorean relationship).
In any triangle ABC,
(the law of cosines).
(We can also write it as or ).
So if = length of side opposite angle A

---> or (rounded)
NOTE:
We can also write the law of cosines as
or .

To find the measure of another angle,
we can apply the law of cosines again,
or we can use the law of sines.
After that, we find the remaining angle by using the fact that the measures of all 3 angles add up to or .

USING LAW OF COSINES AGAIN:
let be the angle opposite the side with length cm.

---> or (rounded).

USING LAW OF SINES FOR A CHANGE:
If you have the measures of one side and the opposite angle of a triangle,
you can apply the law of sines, which states

So, with cm,
--->
(rounded), so
---> or (rounded).

Once we have or
We can find
or
.
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