# Practical Problems

In the topic “Practical Problems”, we will have math problems which are completely based on our real life. In our real life, we people are studying math in school, college and in higher education. In our day to day life, we are facing many situations in which we have to solve many problems by using the concepts of math which we have already studied earlier in school and college.The following practical problems can be solved by using the concept Pythagorean theorem.

We can define Pythagorean theorem as follows. If one of the angle in a measures 90 ° , this kind of triangle is called right triangle. Let ABC be a right triangle in which the measure of angle B = 90°.

The side AC is called the hypotenuse of the right triangle. The side which is opposite to 90 degree is called the hypotenuse side and it is the longest side and is opposite to the right angle. Greek mathematician Pythagoras has found that the length of the square on the hypotenuse is equal to the sum of the length of the squares on the other two sides. That is AC 2 = AB 2 + BC 2. This is knows as Pythagoras theorem.

### Practical problems - solved

Question 1:

A ladder 17 m long touches a window of a house 15 m above the ground level.Determine the distance of the foot of the ladder from house.

Solution:
The below picture represents the information given in the question. AC = ladder = 17 m

AB = height the ladder touches = 15 m

AC 2 = AB 2 + BC 2

BC 2 = AC 2 + AB 2

BC 2 = 172 - 15 2

BC 2 = 289 - 225

BC 2 = 64

BC 2 = √64

BC 2 = √8 x 8

Distance of the foot of the ladder from the house = 8 m

Question 2:

The length of the diagonal of a square is 4√2 m.Find the length of the side.

Solution: Let "a" be the side of the square given.AC = 4√2

In a right angled triangle ABC

AB 2 + BC 2 = AC 2

a 2 + a 2 = (4√2) 2
2a2 = 16 x 2

a 2 = 16

a = √4 x 4

Therefore a = 4

side of the square = 4 m

These are some of the real life usage.Students need to practice this kind of problem to clear understanding.We have also given worksheets to practice this kind of problem.Usually students will have these kind of problems in school grade.All the best

practical problems to Pythagorean theorem

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