Question

10 the sides of a triangle are 17ft., 19ft., and 15 ft. find the measure of the angle opposite the longest side. round your answer to the nearest degree

Answer 1

The law of cosines is used for this purpose. It tells you
  c² = a² + b² - 2ab×cos(C)
Solving for the angle C gives
  C = arccos((a² + b² - c²)/(2ab))
  C = arccos(( 17² + 15² - 19²)/(2×17×15))
  C = arccos(153/510)
  C ≈ 72.5424°

The measure of the angle opposite the longest side is about 73°.