Missing angle of a triangle
Initial explanation
We have that the area of a triangle is given by
Finding a formula
In this case we have that
a = 75
b = 46
and the area is 1653. We want to find C:
Replacing in the formula, we have:
Finding C
We want to solve this equation for C:
Then
We have that arcsin(0.96) have different possible values:
73.7º
106.3º
Since this angle is obtuse (higher than 90º) then, the correct angle for C might be 106.3º
Answer: the measure of the included angle is 106.3º