In triangle ABC, m∠ a=45∘, m∠b65∘, and c=20. Find b. Round your answer to the nearest tenth.

First we find the missing angle which is "C".

We already know they add up to 180º, so that means you add the two given angles that is 45+65 which gives you 110º and then subtract 180-110=70º, C=70º and now you have all three angles and just need to find the side.

To find that side, you'll have to use Sines.

Sin (70) / 20 = Sin (65) / b

cross multiply and you have something like 20 * Sin (65) / Sin (70) = b * Sin (70) / Sin (70)

b = 11.7