Applying Pythagorean Theorem

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Presentation transcript:

Applying Pythagorean Theorem

Baseball Problem A baseball “diamond” is really a square. You can use the Pythagorean theorem to find how far does a catcher have to throw the ball from home plate to second base?

The legs are from home to first and from first to second. Baseball Problem The distance between consecutive bases is 90 feet. How far does a catcher have to throw the ball from home plate to second base? Use the Pythagorean theorem to solve for x. a2 + b2 = c2 Which side is the hypotenuse? Which sides are the legs? The hypotenuse is the distance from home to second, or side x in the picture. The legs are from home to first and from first to second. c2 = a2 + b2 x2 = 902 + 902 x2 = 8100 + 8100 x2 = 16,200 Square Root Each Side x = 127.28 The distance from home plate to 2nd base is 127.28 ft

Ladder Problem A ladder leans against a second-story window of a house. If the ladder is 25 meters long, and the base of the ladder is 7 meters from the house, how high is the window? Distance from house: 7 meters First draw a diagram that shows the sides of the right triangle. Label the sides: Ladder is 25 m Distance from house is 7 m Use a2 + b2 = c2 to solve for the missing side. 72 + b2 = 252 49 + b2 = 625 b2 = 576 b = 24 The height of the window is 24 meters.

Application of Pythagoras’ Theorem 1.A car travels 16 km from east to west. Then it turns left and travels a further 12 km. Find the displacement between the starting point and the destination point of the car. N The hypotenuse is the distance unknown or x in the picture. The legs are the directions 16 km & 12 km c2 = a2 + b2 x2 = 162 + 122 x2 = 256 + 144 x2 = 400 Square Root Each Side x = 20 16km 12km x The car displacement is 20 km SW.

The height of a tree is 5 m. The distance between the top of it and the tip of its shadow is 13 m. 5 m 13 m Find the length of the shadow. Solution: (Pythagoras’ Theorem) c2 = a2 + b2 132 = 52 + x2 x2 = 132 - 52 x2 = 169 - 25 x2 = 144 x = 12 x 13 m 5 m The length of the shadow is 12 m. x

Classwork Page 4ab,5ab,6,7,11,13,16,18