The Pythagorean Theorem is one of the most important results in geometry. It relates the three sides of a right-angled triangle.
It states that for a right-angled triangle with sides a and b (the legs) and hypotenuse c:
This relationship helps us find missing sides in right triangles and solve many real-world problems — such as ladders against walls, distances across fields, and diagonal measurements.
Practice Questions and Answers
A 10 m long ladder leans against a wall. The bottom of the ladder is 6 m from the wall.
At what height does the top of the ladder touch the wall?
We have:
Hypotenuse c=10
Base a=6
Height b=?
By the Pythagorean Theorem:
The ladder touches the wall 8 m above the ground.
A rectangular television screen has a diagonal length of 50 inches and a height of 30 inches.
What is the width of the screen?
Given:
c=50
b=30
a=?
The width of the screen is 40 inches.
A kite is flying with its string making a straight line from the ground.
If the string is 100 m long and the kite is 80 m above the ground, find how far the person holding the string is from the point directly below the kite.
Here,
Hypotenuse (string) c=100
Opposite side (height) b=80
Base (distance from person to point below kite) a=?
The person is 60 m away from the point directly under the kite.
A square field has sides of 25 m. What is the length of the diagonal of the field?
In a square, the diagonal divides the square into two right-angled triangles.
So, if each side is a=25, then the diagonal d is:
The diagonal measures approximately 35.4 m.
A man walks 9 km east and then 12 km north.
Find his shortest distance from his starting point.
The two directions form a right angle.
a=9
b=12
c=?
The shortest distance from the starting point is 15 km.
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Nice emma really precise information.. I appreciate u
Hey Raptor! Thanks very much for the positive feedback, very much appreciated!
explains everything for a child or a confused student in their ap maths class who is lost in the more detailed mathematics
Draw all types of polygon and its area and perimeter class 7th NCERT course
I’m just curious if the area between the polygon and the circumscribed circle has a name.
https://www.superprof.co.uk/resources/academic/maths/geometry/plane/orthocenter-centroid-circumcenter-and-incenter-of-a-triangle.html
Draw all types of polygon and its area and perimeter