Overview
In a right triangle, an acute angle determines fixed ratios between the sides. Given one angle and one side length, the other two sides follow from sine, cosine or tangent, and then the area and perimeter can be computed.
Formula
Opposite = hypotenuse × sin θ, adjacent = hypotenuse × cos θ, and hypotenuse = opposite ÷ sin θ.
How it works
Enter the angle
It must be between 0 and 90 degrees.
Identify the known side
Choose opposite, adjacent or hypotenuse.
Pick the right ratio
Use sin, cos or tan depending on the side.
Compute the rest
Find the other sides, then area and perimeter.
Worked examples
Example 1: angle 30° and opposite side 5
Hypotenuse = 5 ÷ sin 30° = 10, and adjacent ≈ 8.6603.
Example 2: angle 45° and hypotenuse 10
Opposite = adjacent ≈ 7.0711.
Frequently asked questions
How do I identify the opposite side?
It is the side that does not touch the given angle and faces it.
What if the angle is greater than 90°?
This calculator is for right triangles only, whose acute angles are below 90 degrees.
Can I use radians?
Yes, choose radians as the angle unit.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.