SOLUTION: the area of a triangle is 8346 sqm. and two of its interior angles are 37�25' and 56�17'. What is the length of the longest side?

Question 869796: the area of a triangle is 8346 sqm. and two of its interior angles are 37�25' and 56�17'. What is the length of the longest side?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Let's call the missing angle , and the other two angles

and

.
The measure of the third angle is

is the largest angle.

As customary, we call the side opposite each angle (and its length) with the same letter as the opposite angle, but lowercase instead of capital:
= length (in meters) of he longest side (the one opposite largest angle X),
= length (in meters) of he shortest side (the one opposite smallest angle Z), and
= length (in meters) of he medium-sized side (the one opposite medium-sized angle Y).

The sines of the angles rounded to 4 decimal places are:

Law of sines states that
.
Substituting the values of the sines of the angles rounded to 4 decimal places:
.
From those equations we can solve for and as functions of :
-->

We know that the area of a triangle XYZ can be calculated from the length of two sides and the sine of the angle between them as
=
and we know that = square meters
so substituting the values/expressions used/found above,

meters (rounded)
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