Solve a right triangle from two sides — hypotenuse, angles, area
Enter a valid length
Enter a valid length
The right triangle is the workhorse of practical geometry: ramps, roofs, screens, stairs and diagonals are all right triangles in disguise. Give this calculator any two sides — the two legs, or one leg plus the hypotenuse — and it returns the missing side, both acute angles, the area and the perimeter in one pass.
Pick your units (cm, m, in, ft — cosmetic, the ratios are identical), then choose which pair of sides you know. In two-leg mode it applies the Pythagorean theorem to find the hypotenuse. In leg + hypotenuse mode it rearranges the theorem to recover the second leg — and warns you if the hypotenuse is not the longest side, which would make the triangle impossible.
The two acute angles always total 90° — a built-in sanity check on any right-triangle problem.
The classic 3–4–5 triangle: legs of 3 cm and 4 cm give c = √(9 + 16) = 5 cm exactly. Area = 3 × 4 ÷ 2 = 6 cm², perimeter = 12 cm. Angle A = arcsin(3 ÷ 5) ≈ 36.87°, angle B ≈ 53.13°, and indeed they sum to 90°. Scale the triple by ten — 30, 40, 50 — and every result scales with it, which is why builders still use the 3-4-5 rule to square a corner.
| Leg A | Leg B | Hypotenuse | Area |
|---|---|---|---|
| 3 | 4 | 5 | 6 |
| 5 | 12 | 13 | 30 |
| 8 | 15 | 17 | 60 |
| 1 | 1 | √2 ≈ 1.414 | 0.5 |
One caution: the formulas here are exact, but measured inputs are not — a leg measured to the nearest centimetre carries that uncertainty into every result, so keep a margin in real-world cuts.
直角三角形是实用几何的干活主力：坡道、屋顶、屏幕、楼梯和对角线，本质都是直角三角形。给这个计算器任意两条边——两条直角边，或一条直角边加斜边——它一次性给出第三条边、两个锐角、面积与周长。
先选单位（厘米/米/英寸/英尺——只影响显示，比例关系完全一致），再选择你已知的两条边。「两条直角边」模式直接套勾股定理求斜边；「直角边 + 斜边」模式反解出另一条直角边——如果输入的斜边不够长（三角形不成立），会明确报错而不是硬算。
两个锐角之和恒为 90°——这是所有直角三角形题目自带的校验器。
最经典的 3-4-5 三角形：直角边 3 与 4，斜边 c = √(9 + 16) = 5，严丝合缝。面积 = 3 × 4 ÷ 2 = 6，周长 = 12。角 A = arcsin(3 ÷ 5) ≈ 36.87°，角 B ≈ 53.13°，两者之和恰好 90°。把这一组按 10 倍放大——30、40、50——所有结果同步放大，这正是工地师傅至今用 3-4-5 法则放直角的原因。
| 直角边 A | 直角边 B | 斜边 | 面积 |
|---|---|---|---|
| 3 | 4 | 5 | 6 |
| 5 | 12 | 13 | 30 |
| 8 | 15 | 17 | 60 |
| 1 | 1 | √2 ≈ 1.414 | 0.5 |
一点提醒：这里的公式是精确的，但你的测量不是——按厘米取整的边长会把误差带进每个结果，实际下料时记得留余量。
In any right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: c² = a² + b². Legs of 3 and 4 give c = √(9 + 16) = 5 — the most famous whole-number triple.
Rearrange the theorem: b = √(c² − a²). A 5 hypotenuse with a 3 leg gives b = √(25 − 9) = 4. Choose "Leg + hypotenuse" mode and the calculator does the subtraction for you.
Trigonometry: angle A = arcsin(leg A ÷ hypotenuse), angle B = arcsin(leg B ÷ hypotenuse). They always add to 90° — a quick check that the sides you entered form a real right triangle.
Last reviewed: October 5, 2026 · How we calculate · Sources: Pythagorean theorem, standard trigonometry
最近复核：2026 年 10 月 5 日 · 我们的计算方法 · 来源：勾股定理、标准三角函数