Question

A = 16

C = ?
b = 10
In triangle ABC, BC = a = 16, AC = b = 10, and mZC = 22°. Which equation can you use to find the value of c = AB?

Answer 1

c² = a² + b² - 2ab×cos(C)

c = 7.7

Explanation:

we use the enhanced Pythagoras for general triangles :

c² = a² + b² - 2ab×cos(C)

c² = 16² + 10² - 2×16×10×cos(22) = 256 + 100 - 320×cos(22) =

= 356 - 320×0.92718... = 356 - 296.698... ≈ 59.3

c ≈ 7.7

as you can see, the "regular" formula of Pythagoras

c² = a² + b²

is derived from the fact that cos(90)=0.