Pythagores Theorem Application Introduction The Pythagorean

Pythagores Theorem Application

Introduction • The Pythagorean Theorem is one of the most useful formulas in mathematics because there are so many applications of it in out 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

Question #1 To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond? SOLUTION The given question is illustrated in the figure. Given AC=34 m, CB=41 m. To find AB We know that by Pythagorean theorem.

Question #2 Oscar's dog house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across. What is the height of his dog house, in feet, at its tallest point? Solution From the diagram, AB=AC=5, BC=6. To Find AD In ∆ADC, by Pythagorean theorem.

Question #3 How far up a wall will an 11 m ladder reach, if the foot of the ladder must be 4 m from the base of the wall? Solution From the diagram, This figure has been restructured as ∆ABC Given AC=11 m, BC=4 m To find AB by Pythagorean theorem.

Try These • A 24 m long ladder reached a window 25 m high from the ground. On placing it against a wall at a distance x m. Find x. • A rectangular field is of dimension 40 m by 30 m. What distance is saved by walking diagonally across the field?