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**Problem 4.1 Stopping Sneaky Sally**

The Pythagorean Theorem can be used in situations in which you need to find the missing length in a right triangle.

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**Horace Hanson is the catcher for the Humbolt Bees baseball team**

Horace Hanson is the catcher for the Humbolt Bees baseball team. Sneaky Sally Smith, the star of the Canfield Cats, is on first base. Sally is known for stealing bases, so Horace is keeping a sharp eye on her. The pitcher throws a fastball, and the batter swings and misses. Horace catches the pitch. Out of the corner of his eye, he sees Sally take off for second base.

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**How far must Horace throw the baseball to get Sally out at second base**

How far must Horace throw the baseball to get Sally out at second base? Explain how you found your answer. Since that part of the infield makes a right triangle, you need to use the Pythagorean Theorem. a2 + b2 = c2 This is the distance Sally must run = c2 = c2 This is the unknown distance Horace must throw. 16200 = c2 16200 = c2 = c Horace must throw the baseball about 127 feet from home plate to 2nd base.

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Follow up 4.1: The shortstop is standing on the baseline, halfway between second base and third base. How far is the shortstop from Horace? a2 + b2 = c2 = c2 Shortstop = c2 10125 = c2 10125 = c2 = c The shortstop is about 100 feet from the catcher.

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When my 13 foot ladder is set up it reaches the top of my window that is 12 feet in the air. How far from my house is the bottom of my ladder? a2 + b2 = c2 a = 132 a = 169 13’ a2 = 25 12’ a2 = 25 ? a = 5 The ladder is 5 feet from the base of the house.

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When using the Pythagorean theorem, make sure you plug the hypotenuse into “c” in the formula. Make sure you write the formula and show all of your work to get your answer. The Hypotenuse will always be across from the right angle and it will always be the longest of the three sides.

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5.4 The Pythagorean Theorem & Converse Es sential Question: How can we identify and apply the Pythagorean Theorem and its converse by solving problems.

5.4 The Pythagorean Theorem & Converse Es sential Question: How can we identify and apply the Pythagorean Theorem and its converse by solving problems.

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