Pythagorean Theorem Application: Calculate AC in Right Triangle ABC

Triangle ABC is a right triangle,

Find AC

83ABC

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Step-by-step written solution

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1

Understand the problem

Triangle ABC is a right triangle,

Find AC

83ABC

2

Step-by-step solution

To solve this problem, we'll use the Pythagorean Theorem.

  • Step 1: Identify the sides: AB=8 AB = 8 , BC=3 BC = 3 .
  • Step 2: Use the formula: a2+b2=c2 a^2 + b^2 = c^2 , where c c is the hypotenuse (AC).
  • Step 3: Plug in the values: 32+82=AC2 3^2 + 8^2 = AC^2 .
  • Step 4: Calculate: 9+64=AC2 9 + 64 = AC^2 .
  • Step 5: Simplify: 73=AC2 73 = AC^2 .
  • Step 6: Solve for AC AC : AC=73 AC = \sqrt{73} .

Thus, the length of AC is 73 \sqrt{73} .

3

Final Answer

73 \sqrt{73}

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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