Applying Pythagorean Theorem Baseball Problem A baseball diamond

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. a 2 + b 2 = c 2 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. c 2 = a 2 + b 2 x 2 = 902 + 902 x 2 = 8100 + 8100 x 2 = 16, 200 x 2 = 16, 200 (square root each side) x = 127. 28 The distance from home plate to 2 nd 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? First draw a diagram that shows the sides of the right Label the sides: Ladder is 25 m Distance from house is 7 m Use a 2 + b 2 = c 2 to solve for the missing side. 72 + b 2 = 252 49 + b 2 = 625 b 2 = 576 b = 24 Distance from house: 7 meters triangle. The height of the window is 24 meters.

Application of Pythagoras’ Theorem N 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. 16 km 12 km x The hypotenuse is the distance unknown or x in the picture. The legs are the directions 16 km & 12 km c 2 = a 2 + b 2 x 2 = 162 + 122 x 2 = 256 + 144 x 2 = 400 Square Root Each Side x = 20 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. Find the length of the shadow. Solution: (Pythagoras’ Theorem) c 2 = a 2 + b 2 132 = 52 + x 2 = 132 - 52 x 2 = 169 - 25 x 2 = 144 x = 12 The length of the shadow is 12 m. 13 m 5 m x

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