A triangle with angles measuring 45°, 50°, and 85° has sides with lengths of 16.34 cm, 12.57 cm, and 11.60 cm. What is the length of the side opposite the 85° angle?

16.34m

Step-by-step explanation:

Since 85 is the widest angle, it follow that the opposing segment must be the longest.

Assuming this we can verify with the cosine theorem:

c² = a² + b² - 2ab cos (C)

16.34² = 12.57² + 11.60² - 2*11.60*12.57. cos (85°) ?

266.99 = 158.00 + 134.56 - 291.62 * 0.087

266.99 = 266.99

Solving both sides independently, we arrive to the same number, proving our hypothesis