8. RightTriangleTrigonometry.......................................................................................................
The PythagoreanTheorem
LearningObjectives
- Identifyand employthe PythagoreanTheoremwhenworkingwith right triangles.
- IdentifycommonPythagoreantriples.
- Use the PythagoreanTheoremto find the area of isoscelestriangles.
- Use the PythagoreanTheoremto derivethe distanceformulaon a coordinategrid.
Introduction
The trianglebelowis a right triangle.
The sideslabeled and are calledthelegsof the triangleand they meetat the right angle.The third
side,labeled is calledthehypotenuse.The hypotenuseis oppositethe right angle.The hypotenuseof
a right triangleis also the longestside.
The PythagoreanTheoremstatesthat the lengthof the hypotenusesquaredwill equalthe sum of the squares
of the lengthsof the two legs.In the triangleabove,the sum of the squaresof the legs is and the
squareof the hypotenuseis.
The PythagoreanTheorem: Givena right trianglewith legs whoselengthis and
and a hypotenuseof length ,.Be carefulwhenusingthis theorem—youmustmakesure that the legs are labeled and and the hy-
potenuseis labeled to use this equation.A moreaccurateway to writethe PythagoreanTheoremis:
Example 1
Use the side lengthsof the followingtriangleto test the PythagoreanTheorem.