Given
the lengths of the 3 sides of a triangle
Find
the angle opposite the longest side
Solution
Strategy: make use of the Law of Cosines, which relates an angle and the three sides of a triangle.
... a² = b² + c² -2bc·cos(A)
... cos(A) = (b² + c² - a²)/(2bc) . . . . . . . solve for cos(A)
... A = arccos((b² + c² - a²)/(2bc))
Fill in the given values and evaluate.
... A = arccos((55² + 50² - 90²)/(2·55·50)) = arccos(-2575/5500)
... A ≈ 117.9°