1. Pythagoras Theorem Real Time Application

2. 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

3. 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 = =
AB2 = 2837
Ans:- It would have taken Vinod 53.26m to walk from point A to point B

4. 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

5. 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 m in height

6. 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 = AC
AC2 =
AC2 = 25
Ans:- The height of the tree is 5 feet.

7. 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?