SOLUTION: The area of a triangle is 40 cm squared. Find the length of the side included between the angles A=30 degrees and B=50 degrees.

Question 934849: The area of a triangle is 40 cm squared. Find the length of the side included between the angles A=30 degrees and B=50 degrees.
Found 2 solutions by MathLover1, KMST:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Let
= base of the triangle
= altitude of the triangle
Area of a triangle
Therefore, or
........eq. 1
Angle
Using the Law of Sines,

where
= length of the side included between the angles and
Solving for "",
............eq. 2
Since eq.1 = eq.2, then

Solving for ,
OR
since , substitute this in eq.3,

Simplifying the above,

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Let , . and be the sides' lengths, in cm.
-->-->-->
--->
Law of sines says that
,
so --->
---> --->--->--->
So, ---> (rounded)
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