What's the question- what is x?
So for this triangle, since it's not right (No 90° angle, at least not shown), we must use special trigonometric triangles. You may have used Pythagorean Theorem, but you can't unless it's a right triangle.
Now we decide between Law of Sines vs. Law of Cosines. L. of Sines is for when we have 2 angles and one or more sides. L. of Cosines is for when we don't have that 2nd angle, but do have 2 sides... our case here.
Here's how the Law of Cosines works:
[tex]{c}^{2} \: = {a}^{2} + {b}^{2} - (2ab \cos( \gamma )) \\ c = \sqrt{{a}^{2} + {b}^{2} - 2ab \cos( \gamma )} [/tex]
where c is the side needed, a & b are the 2 known sides, and gamma (γ) is the angle opposite the side c.
So a = 21, b = 42, γ = 39°
[tex]c... \: \\ = \sqrt{{21}^{2} + {42}^{2} - 2(21)(42) \cos(39) } [/tex]
[tex]c = \sqrt{441 + 1764 - (1764 \cos(39)) } [/tex]
[tex]c = \sqrt{2205 - (1764)(0.777)} [/tex]
[tex]c = \sqrt{2205 - 1370.89} \\ c = \sqrt{834.11} = 28.88[/tex]
NOPE YOU DID IT CORRECTLY!!
You're "x" = 28.88°
