Pythagorean Theorem: Finding BC in an 8cm × 6cm Right Triangle

Pythagorean Theorem with Known Legs

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

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Step-by-step written solution

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1

Understand the problem

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

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2

Step-by-step solution

To find the length of the hypotenuse BC in a right-angled triangle where AB and AC are the other two sides, we use the Pythagorean theorem: c2=a2+b2 c^2 = a^2 + b^2 .

Here, a=6 cm a = 6 \text{ cm} and b=8 cm b = 8 \text{ cm} .

Plugging the values into the Pythagorean theorem, we get:

c2=62+82 c^2 = 6^2 + 8^2 .

Calculating further:

c2=36+64 c^2 = 36 + 64

c2=100 c^2 = 100 .

Taking the square root of both sides gives:

c=10 cm c = 10 \text{ cm} .

3

Final Answer

10 cm

Key Points to Remember

Essential concepts to master this topic
  • Formula: Use c2=a2+b2 c^2 = a^2 + b^2 where c is the hypotenuse
  • Technique: Calculate 82+62=64+36=100 8^2 + 6^2 = 64 + 36 = 100 , then find square root
  • Check: Verify that 102=82+62 10^2 = 8^2 + 6^2 gives 100 = 64 + 36 ✓

Common Mistakes

Avoid these frequent errors
  • Adding the legs instead of squaring them
    Don't add AB + AC = 8 + 6 = 14 cm! This ignores the square relationship and gives a wrong answer. The hypotenuse is always longer than either leg but shorter than their sum. Always square each leg first, then add the 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.

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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 (90°). In this triangle, BC is opposite the right angle at A, so BC is the hypotenuse we need to find.

Why do we square the sides instead of just adding them?

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The Pythagorean theorem describes a square relationship, not a linear one! Think of it as areas of squares built on each side. The area relationship is c2=a2+b2 c^2 = a^2 + b^2 .

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

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Many triangles don't have nice whole number answers! Use a calculator to find the decimal approximation, or leave your answer as 100 \sqrt{100} if it's not a perfect square.

Can I use this formula for any triangle?

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Only for right triangles! The Pythagorean theorem only works when one angle is exactly 90°. For other triangles, you need different formulas like the Law of Cosines.

How do I remember which sides are a, b, and c?

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The letter c is always the hypotenuse (longest side). Letters a and b can be either of the two shorter sides called legs. It doesn't matter which leg you call a or b!

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