How to Find Hypotenuse Step by Step
If you are studying
geometry, then one of the most basic questions is how to find the hypotenuse
step by step. The hypotenuse is the longest side of a right-angled
triangle. It is always opposite the 90° angle of the triangle. To calculate it
easily, we use the Pythagoras Theorem.
Step 1:
Understand the Right-angled Triangle
A right
triangle has:
- One angle of measure 90°
- Two shorter sides (called legs
or perpendicular sides)
- One longest side (called the
hypotenuse)
The
hypotenuse is always opposite to the right angle.
Step 2:
Learn the Formula
To find the
hypotenuse of the triangle, we use the Pythagoras Theorem:
Where:
- a = first side
- b = second side
- c = hypotenuse
To find the
hypotenuse, we can rearrange the above formula as follows:
This means:
1.
Square
both known sides (legs)
2.
Add
them
3.
Take
the square root of the result
Step 3:
Solve a Simple Example
Find the
hypotenuse of a right-angled triangle whose legs are 6 cm and 8 cm.
Solution:
- One side (a) = 6 cm
- Other side (b) = 8 cm
Now follow
the steps:
1.
Square
both numbers.
6² = 36
8² = 64
2.
Add
them.
36 + 64 = 100
3.
Take
the square root
√100 = 10
So, the
hypotenuse (c) = 10 cm
Step 4:
Try Another Example
If the
perpendicular and base of a right-angled triangle are 5 cm and 12 cm,
respectively, then find its hypotenuse.
Solution: We
have,
- a = 5
- b = 12
1.
Square
both.
5² = 25
12² = 144
2.
Add
them.
25 + 144 = 169
3.
Find
square root
√169 = 13
So, the
hypotenuse is 13 cm.
Important
Tips
✔ The formula only works for right-angled
triangles.
✔ Always check that one angle is 90°.
✔ Square first, then add, then take square root.
✔ The hypotenuse is always the longest side and it is opposite
the 90° angle.
Real-Life
Applications
Finding the
hypotenuse is useful in:
- Construction and architecture
- Measuring distance
- Navigation and mapping
- Computer graphics
- Physics problems
For example,
if you know the height and base of a ladder leaning against a wall, you can
calculate the ladder’s length using this method.
Conclusion
Now, you
know how to find the hypotenuse step by step. Just remember the formula:
Where, c is the hypotenuse and a and b
are legs of the triangle.
Square both legs, add them, and take the square root. With practice, solving these problems becomes quick and easy. Geometry may look difficult at first, but with clear steps and examples, you can master it confidently.