Calculate Triangle Side AC: Using 3-4 Right Triangle Measurements

Pythagorean Theorem with Basic Integer Values

Look at the triangle in the diagram. Calculate the length of side AC.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find AC
00:03 We'll use the Pythagorean theorem in a right triangle
00:08 We'll substitute appropriate values and solve for AC
00:21 Take the square root
00:28 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the triangle in the diagram. Calculate the length of side AC.

333444AAABBBCCC

2

Step-by-step solution

To solve the exercise, we have to use the Pythagorean theorem:

A²+B²=C²

 

We replace the data we have:

3²+4²=C²

9+16=C²

25=C²

5=C

3

Final Answer

5 cm

Key Points to Remember

Essential concepts to master this topic
  • Pythagorean Rule: In right triangles, a² + b² = c² where c is hypotenuse
  • Technique: Calculate 3² + 4² = 9 + 16 = 25, then √25 = 5
  • Check: Verify 5² = 25 equals 3² + 4² = 9 + 16 = 25 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing which side is the hypotenuse
    Don't assume the longest given side is always c in the formula! This leads to wrong calculations like 4² + 5² = 3². Always identify the hypotenuse as the side opposite the right angle (the longest side).

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.

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FAQ

Everything you need to know about this question

How do I know which side is the hypotenuse?

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The hypotenuse is always the longest side and sits opposite the right angle (the 90° corner). In this triangle, AC is opposite the right angle at B, making it the hypotenuse.

Why is it 3² + 4² and not 3 + 4?

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The Pythagorean theorem requires squaring each leg, not just adding them. Think of it as finding the area of squares built on each side: 3² = 9 square units, 4² = 16 square units.

What if I don't get a perfect square root?

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Many triangles give irrational numbers like 13 \sqrt{13} . The 3-4-5 triangle is special because it gives a whole number answer - that's why it's called a Pythagorean triple!

Can I use this formula for any triangle?

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No! The Pythagorean theorem only works for right triangles. You must have a 90° angle. For other triangles, you need different formulas like the Law of Cosines.

How do I remember the 3-4-5 pattern?

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The 3-4-5 triangle is the most common Pythagorean triple. Remember it as a scaling pattern: 6-8-10, 9-12-15, etc. All follow the same ratio!

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