Question

Solve each triangle. Round your answers to the nearest tenth

Answer 1

You have to use the Law of Cosines here, since there's no other way to solve this.  it's not a right triangle, so you can't use the Pythagorean Theorem.  The Law of Cosines will help us find the missing side length then we will have to use the Law of Sines to find another angle.  Then after that we will use the Triangle Angle-Sum theorem to finish it off.  Ready? The Law of Cosines to find side b is$b^{2} = a^{2}+ c^{2} -2ac cosB$ and fill in the info we know, which is everything but the b. $b^{2} =(21) ^{2} +(29) ^{2} -2(21)(29)cos109$. Doing all that math gives us that side b = 40.9 or 41. Now the Law of Sines to find missing angle A or C.  Let's find A. $\frac{sinA}{21} = \frac{sin109}{41}$.  That gives us that angle A is 29.  Now use the fact that all triangles add up to 180 to get that angle C is 42.  And you're done!