📐 Right Triangle Side and Angle Calculator
Calculate all sides and angles from one side and one angle
How to Use This Calculator
Select Side Type
Choose whether the known side is a leg (perpendicular side) or the hypotenuse.
Enter Side Length
Input the length of the known side. Make sure it's a positive number.
Enter Angle
Input the known angle (in degrees). It must be between 0° and 90°.
Calculate
Click "Calculate" to find all remaining sides, angles, area, and perimeter using trigonometry.
Formula
Given Leg and Angle:
- Other Leg = Leg × tan(angle)
- Hypotenuse = Leg / cos(angle)
- Other Angle = 90° - given angle
Given Hypotenuse and Angle:
- Leg 1 = Hypotenuse × sin(angle)
- Leg 2 = Hypotenuse × cos(angle)
- Other Angle = 90° - given angle
Trigonometric Functions:
- sin(θ) = opposite / hypotenuse
- cos(θ) = adjacent / hypotenuse
- tan(θ) = opposite / adjacent
About Right Triangle Side and Angle Calculator
The Right Triangle Side and Angle Calculator finds all properties of a right triangle when you know one side length and one angle (other than the 90° angle). It uses trigonometric functions (sine, cosine, tangent) to calculate the remaining sides and angles.
When to Use This Calculator
- Trigonometry: Solve problems with one side and one angle known
- Construction: Calculate dimensions when angle is measured
- Education: Learn trigonometric relationships in right triangles
- Engineering: Design calculations with angular constraints
Why Use Our Calculator?
- ✅ Trigonometry-Based: Uses sine, cosine, and tangent functions
- ✅ Flexible Input: Works with leg or hypotenuse
- ✅ Complete Results: Finds all sides, angles, area, and perimeter
- ✅ Educational: Helps understand trigonometric relationships
- ✅ Free: No registration required
Key Concepts
- SOH CAH TOA: Mnemonic for sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent
- Complementary Angles: The two non-right angles sum to 90°
- Angle Range: Known angle must be between 0° and 90° (exclusive)
Frequently Asked Questions
Can I use this if I know the 90° angle?
No, you need to know one of the other two angles (the acute angles). The 90° angle is always present in a right triangle.
What if I know two sides instead?
Use the regular Right Triangle Calculator which works with two known sides. This calculator is specifically for one side and one angle.
Which angle should I use?
You can use either of the two acute angles. The calculator will automatically find the other angle (which equals 90° - given angle).
Why can't the angle be 90°?
If the angle is 90°, you'd need to know which side is opposite it (the hypotenuse), but then you'd still need another measurement. Use the Right Triangle Calculator with two sides instead.