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14.6 Pythagorean Theorem
1) What triangle is used for the theorem?
2) Define the parts of this triangle
- 1) The theorem deals with the applications of Right triangle
- 2) Hypotenuse - longest side of the triangle
- Other two sides are called legs
- One right angle is present
State the Phythagorean Theorem
- In any right triangle, if a and b are the lengths of the legs and c is the length of the hypotenuse then
- a2 + b2 = c2
- This is called the Pythagorean equation
State the steps used to solve word problems involving the Pythagorean theorem
- 1) read the problem and familarize yourself - visualize and draw the right triangle
- 2) translate this to the pythagorean theorem
- 3) solve the equation - remembering to deal with the square - take sqaure root to solve for base number
- 4) check your solution by plugging it into the equation
Solve the word problem
Dimensions of a softball Diamond
A womens fast pitch softball diamond is actually a square 60ft on a side. How far is it from home plate to second base?
Give an exact answer and an approximation to three decimal places.
- 1) Familarize your self - Make a drawing. Note that the first and second baselines, together with a line from home to second,
- form a right triangle. Label the unknown distance d
- 2) translate - use pythagorean equation
- a2 + b2 = c2
- 602 + 602 =d2 3) solve the equation
- 3600+3600= d2
- 7200 = d2
- 4) Check - check calculations using the pythagorean equation:
- 602 + 602 = 7200 and (84.853)2 = 7200