Example 1: Finding the hypotenuse
\(a = 3, b = 4 \rightarrow c^2 = 3^2 + 4^2 = 9 + 16 = 25 \rightarrow c = \sqrt{25} = 5\)
ピタゴラスの定理
ピタゴラスの定理を使って直角三角形の欠けている辺の長さを求めます
結果
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理論と公式
The Pythagorean theorem is a fundamental principle in geometry that relates the sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
This theorem only applies to right triangles (triangles with one 90-degree angle). The hypotenuse is always the longest side and is opposite the right angle.
Common Pythagorean Triples
- 3, 4, 5 (and multiples: 6, 8, 10; 9, 12, 15; etc.)
- 5, 12, 13
- 8, 15, 17
- 7, 24, 25
- 9, 40, 41
\(a^2 + b^2 = c^2\)
解説付き例題
Example 2: Finding a leg
\(a = ?, b = 8, c = 10 \rightarrow a^2 = 10^2 - 8^2 = 100 - 64 = 36 \rightarrow a = \sqrt{36} = 6\)