Calculate Side AB in a Right Triangle: Given Sides 2 and 3

Q: How do I know which side is the hypotenuse?

The hypotenuse is always the longest side and is opposite the right angle. In this diagram, AB is diagonal across from the right angle at C, making it the hypotenuse.

Q: Why can't I just add the two sides together?

Triangle sides follow the Pythagorean relationship, not simple addition! If you added 3 + 2 = 5, you'd get the wrong answer. The correct method squares each leg first.

Q: What if I get a decimal instead of a square root?

Both forms are correct! $ \sqrt{13} $ is the exact answer, while 3.606... is the decimal approximation. Usually, leave answers in radical form unless asked for decimals.

Q: How do I calculate square roots like √13?

For non-perfect squares like $ \sqrt{13} $, leave it in radical form as your final answer. You can use a calculator to get 3.606 if needed, but $ \sqrt{13} $ is more precise.

Q: Can I use this method for any right triangle?

Yes! The Pythagorean theorem works for all right triangles. Just remember: if you know two sides, you can always find the third using $ a^2 + b^2 = c^2 $.

Pythagorean Theorem with Given Legs

Look at the triangle in the diagram. How long is side AB?

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Step-by-step video solution

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Step-by-step written solution

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Understand the problem

Look at the triangle in the diagram. How long is side AB?

Step-by-step solution

To find side AB, we will need to use the Pythagorean theorem.

The Pythagorean theorem allows us to find the third side of a right triangle, if we have the other two sides.

You can read all about the theorem here.

Pythagorean theorem:

$A^2+B^2=C^2$

That is, one side squared plus the second side squared equals the third side squared.

We replace the existing data:

$3^2+2^2=AB^2$

$9+4=AB^2$

$13=AB^2$

We find the root:

$\sqrt{13}=AB$

Final Answer

$\sqrt{13}$ cm

Key Points to Remember

Essential concepts to master this topic

Rule: In right triangles, $a^2 + b^2 = c^2$ where c is hypotenuse
Technique: Substitute known values: $3^2 + 2^2 = 9 + 4 = 13$
Check: Verify $(\sqrt{13})^2 = 13$ and 13 = 9 + 4 ✓

Common Mistakes

Avoid these frequent errors

Adding the two given sides instead of using Pythagorean theorem
Don't simply add 3 + 2 = 5! This gives a completely wrong answer because triangle sides don't follow simple addition. Always use $a^2 + b^2 = c^2$ and take the square root of the sum of squares.

Practice Quiz

Test your knowledge with interactive questions

Consider a right-angled triangle, AB = 8 cm and AC = 6 cm.
Calculate the length of side BC.

FAQ

Everything you need to know about this question

How do I know which side is the hypotenuse?

The hypotenuse is always the longest side and is opposite the right angle. In this diagram, AB is diagonal across from the right angle at C, making it the hypotenuse.

Why can't I just add the two sides together?

Triangle sides follow the Pythagorean relationship, not simple addition! If you added 3 + 2 = 5, you'd get the wrong answer. The correct method squares each leg first.

What if I get a decimal instead of a square root?

Both forms are correct! $\sqrt{13}$ is the exact answer, while 3.606... is the decimal approximation. Usually, leave answers in radical form unless asked for decimals.

How do I calculate square roots like √13?

For non-perfect squares like $\sqrt{13}$ , leave it in radical form as your final answer. You can use a calculator to get 3.606 if needed, but $\sqrt{13}$ is more precise.

Can I use this method for any right triangle?

Yes! The Pythagorean theorem works for all right triangles. Just remember: if you know two sides, you can always find the third using $a^2 + b^2 = c^2$ .

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Calculate Side AB in a Right Triangle: Given Sides 2 and 3

Pythagorean Theorem with Given Legs

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I know which side is the hypotenuse?

Why can't I just add the two sides together?

What if I get a decimal instead of a square root?

How do I calculate square roots like √13?

Can I use this method for any right triangle?

🌟 Unlock Your Math Potential

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