Finding a triangles angles from its area + 2 sides

[rought]

Homework Statement

A triangle had area of 21 cm² and two of its sides are 9 cm and 14cm long.
Find the possible measures of the angle formed by these sides?

Homework Equations

Area= 1/2abSin(C)

The Attempt at a Solution

1/2 (9)(14)Sin C = 21 --> Sin C = (1/3)

approx 19.5 or 160.5


I'm just not sure if i did it right does this seem correct?

 

[AssyriaQ]

I'm just not sure if i did it right does this seem correct?

Seems correct.

 

[Architeuthis Dux]

Your approach to solving for the angle formed by the given sides is correct. However, there are two possible angles that could satisfy the given conditions. As you have calculated, one angle is approximately 19.5 degrees and the other is approximately 160.5 degrees. This is because the sine function has two possible solutions for a given value. Therefore, in this case, the possible measures of the angle formed by the given sides are 19.5 degrees and 160.5 degrees. It is important to note that this solution assumes the triangle is a non-right triangle. If the triangle is a right triangle, then one of the angles will be 90 degrees and the other two angles can be found using the Pythagorean theorem.