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DO NOW!!! Solve for the missing side in each right triangle below. Remember: a2 + b2 = c2 2.) 1.) c 5 40 b 12 24 DO NOW!!! ANSWERS Solve for the missing side in each right triangle below. Remember: a2 + b2 = c2 2. 1. c 5 40 b 12 C = 13 24 B = 32 PYTHAGOREAN THEOREM WORD PROBLEMS OBJECTIVE: Students will solve for missing values using the Pythagorean theorem for word problems RECALL THE PYTHAGOREAN THEOREM THE PYTHAGOREAN THEOREM STATES THAT FOR ANY RIGHT TRIANGLE: 2 a + 2 b = 2 c WORD PROBLEMS!! Most Pythagorean Theorem Questions are given as word problems. STEPS FOR SOLVING PYTHAGOREAN THEOREM WORD PROBLEMS: Step 1: Circle any important numbers in the problem Step 2: Draw a picture of the situation. Step 3: Solve using the Pythagorean theorem (a2 + b2 = c2) EXAMPLE 1!! You're locked out of your house and the only open window is on the second floor, 25 feet above the ground. You need to borrow a ladder from one of your neighbors. There's a bush along the edge of the house, so you'll have to place the ladder 10 feet from the house. What length of ladder do you need to reach the window? 25 feet Step 1: Circle Important numbers. Step 2: Draw a picture of the situation. 10 feet EXAMPLE 1!! You're locked out of your house and the only open window is on the second floor, 25 feet above the ground. You need to borrow a ladder from one of your neighbors. There's a bush along the edge of the house, so you'll have to place the ladder 10 feet from the house. What length of ladder do you need to reach the window? 25 feet STEP 3: PYTHAGOREAN THEOREM a2 + b2 = c2 102 + 252 = c2 100 + 625 = c2 725 = c2 C = 26.92 feet 10 feet EXAMPLE 2!! Step 1: Circle Important numbers. Step 2: Draw a picture of the situation. STEP 3: PYTHAGOREAN THEOREM a2 + b2 = c2 362 + 242 = c2 1296 + 576 = c2 1872 = c2 C = 43.26 inches 24 inches Mr. Young is measuring his TV. The TV is 36 inches wide and 24 inches tall. What is the length of the diagonal on the TV? 36 inches EXAMPLE 3!! Step 1: Circle Important numbers. Step 2: Draw a picture of the situation. STEP 3: PYTHAGOREAN THEOREM a2 + b2 = c2 282 + b2 = 402 784 + b2 = 1600 b2 = 816 b = 28.57 feet 28 feet Firefighters have a 40 foot extension ladder. In order to reach 28 feet up a building, how far away from the building should the foot of the ladder be placed? b PRACTICE PROBLEMS TRY THE FOLLOWING PRACTICE PROBLEMS TO BE COLLECTED AND GRADED AT THE END OF THE PERIOD. IF YOU FINISH EARLY, TRY THE BONUS PROBLEMS WORTH 5 bonus POINTS EACH.