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?

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  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