Chapters
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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