geometry · worked example

Solve 兩股長為 3 和 4 的直角三角形 — c = 5

Method: 畢氏定理. Verified step-by-step solution with our free AI math solver.
Problem

a2+b2=c2, a=3, b=4a^2 + b^2 = c^2,\ a=3,\ b=4

Step-by-step solution

  1. 確認直角三角形的兩股:a=3a = 3b=4b = 4

  2. 套用畢氏定理:a2+b2=c2a^2 + b^2 = c^2,其中 cc 為斜邊。

  3. 代入已知數值:32+42=c23^2 + 4^2 = c^2

  4. 計算平方:9+16=c29 + 16 = c^2,因此 c2=25c^2 = 25

  5. 取正平方根(長度為正):c=5c = 5

  6. 3-4-5 三角形是最小的畢氏三元數組——在作業與標準化測驗中很常見。

Answer

c=5c = 5

Want to solve a different problem? Open the pythagorean-theorem solver →