1. Pythagoras Theorem Application

2. 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

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

4. Example 2: Oscar's dog house is shaped like a tent
Example 2: Oscar's dog house is shaped like a tent.  The slanted sides are both 5 m long and
the bottom of the house is 6 m across.  What is the height of his dog house, in feet, 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 dogs house is 4m

5. from the base of the wall?
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 m in height

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