In a triangle

Question

in Triangle ABC side a is 18cm long side b is 10cm long and angle b is 89 degrees what is the measure of angle a

Answer 1

sinA/a=sinB/b (sine rule) so sinA/18=sin89/10=0.1000; sinA=18sin89/10=1.8 which is not possible because sine cannot exceed 1. However, C can be 89 degrees. Let's assume this. However, we don't know side c, but we can find it using the cosine rule; c^2=a^2+b^2-2abcosC=324+100-360cos89=417.7171, c=20.433. Now we can use the sine rule: sinA/a=sinC/c=0.04892 and sinA=0.8806, A=61.71º.