Right Triangle Side and Angle Calculator
Calculate all sides and angles from one side and one angle
Instructions
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)
Common 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.