Question

Solve the triangle (c, A,B)
a=5
b=6
C=70degrees

Answer 1

Are you familiar with the Cosine rule?

\[a^2=b^2+c^2-2bc CosA\]

Answer 2

You can use sine law and cosine law to solve the triangle.
As you have 2 sides with an included angle, you can apply cosine law first.
c^2 = a^2 +b^2 -2abcosC
= 5^2 + 6^2 - 2(5)(6)cos 70
c = 6.36
Then, you can apply sine law to get the rest of the unknowns
sinA sinC a sinC 5sin70
---- = ----- => sinA = ------ = ------ => A = 47.6
a c c 6.36
Can you find out the last angle (angle B) ?

Answer 3

You can use the above method to find angle B, or use angle sum of triangle to find it.
Note that angle sum of triangle is
angle A + angle B + angle C =180 degrees