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

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°.