11 - triangle geometry

Question 1

sine rule

Answer 1

a/sinA = b/sinB = c/sinC
sinA/a = sinB/b + sinC/c
- need an angle the opposite side and another side/angle
- could be two answers as sin(x) = sin(180 - x) - use each one if theta is specified to be acute or obtuse

Question 2

cosine rule

Answer 2

a^2 = b^2 + c^2 - 2bc cosA
cos A = b^2 + c^2 - a^2 / 2bc
- if you have 3 sides or two sides and the included angle
- no second solution as cos(x) only has one solution between 0 and 180

Question 3

area of a triangle

Answer 3

1/2 base * height
1/2 ab sinC
- if you know two sides and angle between