Pythagoras Theorem Real Time Application

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Presentation transcript:

Pythagoras Theorem Real Time Application

Introduction The Pythagorean Theorem is one of the most useful formulas in mathematics because there are so many applications of it in the world. Some examples: Architects and engineers use this formula extensively when building ramps Painting on a Wall Crossing the pond in shortest way Constructing a tent

Ans:- It would have taken Vinod 53.26m to walk from point A to point B Example 1: To avoid a pond, Vinod walked from point A to 34 meters south point C and then 41 meters east to point B. Find how many meters it would have taken for Vinod if he had gone from point A to Point B Solution Given: AC= 34m, CB = 41m. To find: AB AB2 = AC2 + CB2 (Pythagorean theorem) AB2 = 342 + 412 = 1156 + 1681 AB2 = 2837 Ans:- It would have taken Vinod 53.26m to walk from point A to point B

Ans:- The height of dog’s house is 4m Example 2: Oscar's dog’s house is shaped like a tent. The slanted sides are both 5 m long and the bottom of the house is 6 m. What is the height of the dog’s house, at its tallest point? Solution : Given: AC = 5m , AB = 5 m, BD = 3m ,DC = 3m To find: AD AC2 = AD2 + DC2 (Pythagorean theorem) AD2 = AC2 - DC2 AD2 = 52 – 32 AD2 = 25 – 9 AD2 = 16 Ans:- The height of dog’s house is 4m

Ans:- The ladder will reach 10.24 m in height Example3: How far up a wall will an 11m ladder reach, if the foot of the ladder must be 4m from the base of the wall? Solution: From the diagram, this figure has been restructured as ∆ABC Given: AC=11m, BC=4m To find: AB AC2 = AB2 + BC2 (Pythagorean theorem) AB2 = AC2 - BC2 AB2 = 112 – 42 AB2 = 121 – 16 AB2 = 105 Ans:- The ladder will reach 10.24 m in height

Example4 : A tree casts a shadow that is 12 feet long. The distance from the tip of the tree to the tip of the shadow is 13 feet. What is the height of the tree? Solution: Given: AB = 13 feet , BC = 12 feet To find: AC AB2 = AC2 + CB2 (Pythagorean theorem) 132 = AC2 + 122 AC2 = 169 - 144 AC2 = 25 Ans:- The height of the tree is 5 feet.

Try These A 24 cm long ladder reached a window 26 cm high from the ground. On placing it against a wall at a distance x cm. Find x. A rectangular field is of dimension 18m by 24m. What distance is saved by walking diagonally across the field?