How to Solve for Side C Using the Pythagorean Theorem with Sides 8 in and 2 in

Step-by-step guide to calculate the length of side C using the Pythagorean theorem when sides 8 inches and 2 inches are known.

PDF

The Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. The theorem states that:

a2 + b2 = c2

where c is the hypotenuse (the side opposite the right angle), and a and b are the other two sides.

Given:

  • a = 8 inches
  • b = 2 inches
  • Find: c

Step-by-step solution:

  1. Square both sides:
    a2 = 82 = 64
    b2 = 22 = 4
  2. Sum the squares:
    a2 + b2 = 64 + 4 = 68
  3. Take the square root to find c:
    c = √68
  4. Simplify the square root if possible:
    √68 = √(4 × 17) = 2√17 ≈ 8.246 inches

Answer:

Side c is approximately 8.25 inches.

Ask a followup question