全面的直角三角形計算器，包含視覺化圖表、三角表、幾何見解和畢達哥拉斯三重檢測，適合學生和專業人士。
基部（腿 a）
3.000
單位
身高（腿 b）
4.000
單位
斜邊
5.000
單位
區域
6.000
平方單位
週長
12.000
三角形周圍的單位
寬高比
1.333
高度÷底邊
海拔和半徑
- 海拔高度與斜邊之比
- 2.400
- 內切圓半徑
- 1.000
- 外接圓半徑
- 2.500
比例
- 腿長比（b ÷ a）
- 1.333
- 腿長差異
- 1.000
- 互餘角
- 53.13° / 36.87°
縮放三角形圖
圖表以最長腿的比例縮放，以便進行視覺比較。
角度 + 三角函數分解
| 角度 | 測量值（°） | 正弦 | 餘弦 | 切線 |
|---|---|---|---|---|
| ∠A (base ↔ hypotenuse) | 53.130 | 0.8000 | 0.6000 | 1.3333 |
| ∠B (height ↔ hypotenuse) | 36.870 | 0.6000 | 0.8000 | 0.7500 |
| ∠C (right angle) | 90.000 | 1.0000 | 0.0000 | — |
幾何學見解
-
Scalene right triangle
All three sides differ in length, leading to complementary acute angles.
-
Pythagorean triple detected
Side lengths closely match the 3-4-5 integer triple.
-
Shape proportion
The triangle is taller than it is wide with an aspect ratio of about 1.33:1.
-
Inradius and altitude
The inscribed circle radius is 1.000 and the altitude to the hypotenuse is 2.400.
快速參考
- 直角三角形的面積永遠是底乘以高的一半。
- 利用正弦和餘弦函數從斜邊投影出其他任意長度。
- 互餘銳角之和總是90°。知道其中一個角，另一個角就自然而然地就出來了。
Solve any right triangle instantly with our comprehensive calculator that finds missing sides, angles, area, perimeter, and advanced geometric properties. Perfect for students, engineers, architects, and anyone working with trigonometry and geometry calculations.
Advanced Features:
- Complete Triangle Analysis: Calculate all sides, angles, area, perimeter, and altitude from any two known values
- Visual Diagram: Scaled triangle representation with proportional accuracy and angle markings
- Trigonometry Table: Complete sine, cosine, and tangent values for all angles
- Pythagorean Triple Detection: Automatically identifies integer triangle relationships
- Geometry Insights: Provides aspect ratios, complementary angles, and shape analysis
- Circle Properties: Calculates inscribed and circumscribed circle radii
Perfect for:
- Students learning geometry, trigonometry, and the Pythagorean theorem
- Engineers & Architects requiring precise triangle calculations for structural design
- Educators teaching geometric concepts with visual demonstrations
- Professionals in construction, surveying, and technical fields
How It Works: Simply input any two known values (sides or angles) and our right triangle solver instantly calculates all remaining properties. The tool handles various input combinations including base and height, hypotenuse and angle, or any side-angle pairs.
Mathematical Foundation: Built on fundamental geometric principles including the Pythagorean theorem (a² + b² = c²), trigonometric ratios (sine, cosine, tangent), and triangle area formulas. Our calculator ensures accuracy for academic work, professional projects, and real-world applications.
Unique Benefits:
- Instant Results: No complex formulas to remember
- Visual Learning: Scaled diagrams enhance understanding
- Complete Solutions: More than basic calculators - includes advanced properties
- Educational Value: Geometry insights explain triangle relationships
Start solving your right triangle problems today with our free, comprehensive calculator tool.