How to Use the Trig Ratio Calculator
This calculator finds all trigonometric ratios (sin, cos, tan) and angles of a right triangle from any two known sides. Both degrees and radians are shown. Useful for math class, physics, and engineering.
Trigonometric Ratios
For angle A (at the adjacent side): sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent. These ratios depend only on the angle, not the triangle's size.
How It Works
Given two sides, the Pythagorean theorem (a²+b²=c²) finds the third. Then inverse trig (arctan) computes the acute angles. The right angle is always 90°, so both acute angles add to 90°.
Input Rules
All side lengths must be positive. The hypotenuse must be the longest side. If you select hypotenuse as one of the known sides, the other side entered must be shorter than the hypotenuse.
Frequently Asked Questions
They are used in navigation, architecture, physics (inclined planes, oscillations), engineering design, and computer graphics. They connect angles and distances in any right-triangle situation.
Degrees are intuitive for everyday use; radians are required in calculus and programming (Math.sin/cos in most languages use radians). Showing both saves a conversion step.
Yes. As angle A approaches 90°, tan A approaches infinity. This happens when opposite b is much larger than adjacent a. The calculation remains valid for any positive side lengths.