Question

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

Answer 1

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