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Pythagorean Theorem - Finding Lengths in Right Triangles

Learn how to use the Pythagorean theorem to find the length of the hypotenuse or one of the legs in a right triangle. Practice solving examples and identify right triangles.

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Pythagorean Theorem - Finding Lengths in Right Triangles

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  1. Transparency 4 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 4-4b Objective Use the Pythagorean Theorem

  4. Example 4-4b Vocabulary Right triangle A triangle with one right angle (900)

  5. Example 4-4b Vocabulary Legs The sides that form the right angle Legs

  6. Example 4-4b Vocabulary Hypotenuse The side opposite the right angle (it is the longest side) Hypotenuse

  7. Example 4-4b Vocabulary Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs C2 = A2 + B2

  8. Example 4-4b Vocabulary Converse If the sides of a triangle have lengths a, b, and c units such that C2 = A2 + B2 , then the triangle is a right triangle

  9. Lesson 4 Contents Example 1Find the Length of the Hypotenuse Example 2Find the Length of a Leg Example 3Use the Pythagorean Theorem Example 4Identify a Right Triangle

  10. Example 4-1a KITES Find the length of the kite string. Write the Pythagorean Theorem formula Will be solving for c Replace a with 5 Replace b with 12 Follow order of operations P E MD AS Solve all exponents 1/4

  11. Example 4-1a KITES Find the length of the kite string. Add Ask “What is being done to the variable”? Variable is being squared Do the inverse on both sides of the = sign Find square root of both sides Remember: The answer could be negative or positive 1/4

  12. Example 4-1a Since it is a measurement the answer cannot be negative Add dimensional analysis Answer: c = 13 feet 1/4

  13. Example 4-1b KITES Find the length of the kite string. Answer: c = 26 ft 1/4

  14. Example 4-2a The hypotenuse of a right triangle is 33 centimeters long and one of its legs is 28 centimeters. Find the length of the other leg. Draw and label the triangle Draw right triangle Label hypotenuse 33 cm 33 cm Label a leg 28 cm 28 cm Remember: Do not have to distinguish between legs a Label other leg as a Write Pythagorean Formula Replace c with 33 Bring down = a2 + Replace b with 28 2/4

  15. Example 4-2a The hypotenuse of a right triangle is 33 centimeters long and one of its legs is 28 centimeters. Find the length of the other leg. Draw and label the triangle Follow order of operations P E MD AS Solve all exponents Ask: “What is being done to the variable?” Variable is being added by 784 Do the inverse on both sides of the = sign 2/4

  16. Example 4-2a The hypotenuse of a right triangle is 33 centimeters long and one of its legs is 28 centimeters. Find the length of the other leg. Draw and label the triangle Subtract on each side of the = sign Ask: “What is being done to the variable?” Variable is being squared Do the inverse on both sides of the = sign = a 17.46 or -17.46 Find square root of both sides 2/4

  17. Example 4-2a The hypotenuse of a right triangle is 33 centimeters long and one of its legs is 28 centimeters. Find the length of the other leg. Draw and label the triangle 17.46 or -17.46 = a Since it is a measurement the answer cannot be negative 17.46 = a Add dimensional analysis Answer: a = 17.46 centimeters 2/4

  18. Example 4-2b The hypotenuse of a right triangle is 26 centimeters long and one of its legs is 17 centimeters. Find the length of the other leg. Draw and label the triangle Answer: a = 19.67 centimeters 2/4

  19. Example 4-3a MULTIPLE–CHOICE TEST ITEMA 10–foot ramp is extended from the back of a truck to the ground to help movers load furniture onto the truck. If the ramp touches the ground at a point 9 feet behind the truck, how high off the ground is the top of the ramp? A about 1 foot B about 4.4 feet C about 13.5 feet D about 19 feet Draw a ramp that is a right triangle 10 ft a ft 9 ft Label triangle 3/4

  20. Example 4-3a a Write Pythagorean Formula Replace c with 10 Bring down = a2 + Replace b with 9 3/4

  21. Example 4-3a Follow order of operations P E MD AS Solve all exponents Ask: “What is being done to the variable?” Variable is being added by 81 Do the inverse on both sides of the = sign Subtract on each side of the = sign Ask: “What is being done to the variable?” Variable is being squared Do the inverse on both sides of the = sign 3/4

  22. Example 4-3a Find square root of both sides Since it is a measurement the answer cannot be negative Choose the appropriate answer A about 1 foot B about 4.4 feet C about 13.5 feet D about 19 feet 4.36 or - 4.36 = a 4.36 = a Answer: B 3/4

  23. Example 4-3b MULTIPLE–CHOICE TEST ITEMThe base of a 12–foot ladder is 5 feet from the wall. How high can the ladder reach? A about 7 feet B about 10.9 feet C about 11.8 feet D about 13 feet Answer: B 3/4

  24. Example 4-4a The measures of three sides of a triangle are 24 inches, 7 inches, and 25 inches. Determine whether the triangle is a right triangle. Write Pythagorean Formula The hypotenuse is the longest side so replace c with 25 A is the shortest side so replace a with 7 Replace b with 24 Find the powers on each side Add Are both sides equal? Answer: The triangle is a right triangle. 4/4

  25. Example 4-4b * The measures of three sides of a triangle are 13 inches, 6 inches, and 12 inches. Determine whether the triangle is a right triangle. Answer: no, the triangle is not a right triangle 4/4

  26. End of Lesson 4 Assignment

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