Trigonometry Calculator — Right Triangle Solver
Enter one acute angle and one side length — opposite, adjacent, or hypotenuse — and this calculator solves the entire right triangle: all three sides, the complementary angle, and the values of sin, cos, and tan for your angle.
°
Known side
Longest side, opposite the right angle
- 1
Angle in radians
35° × π ÷ 180 = 0.610865 - 2
sin A
sin(0.610865) = 0.573576 - 3
Hypotenuse c (given input)
10The hypotenuse is the known side; sin A and cos A are used to compute legs a and b.
How does this calculator work?
Enter angle A (0°–90°) and one known side. The calculator applies sin A = a/c, cos A = b/c, or tan A = a/b to find the missing sides, then confirms with a² + b² = c². The complementary angle B = 90° − A. Great for geometry homework, surveying, and construction layout.
Formula
How this is calculated
A right triangle has one 90° angle. The other two acute angles (A and B) always add to 90°, so knowing one gives the other immediately. The three sides are the opposite (a, across from angle A), the adjacent (b, next to angle A), and the hypotenuse (c, opposite the right angle).
The three primary trig ratios — SOH CAH TOA — express each pair of sides as a ratio: sin A = a/c, cos A = b/c, tan A = a/b. Rearranging any of these lets you calculate an unknown side from a known side and angle. For example, if you know the angle and hypotenuse, a = c × sin A and b = c × cos A. If you know angle and opposite side, c = a / sin A.
This calculator applies whichever rearrangement matches your inputs and verifies the result against the Pythagorean theorem a² + b² = c². The visualization shows the three squares on the sides, illustrating why the hypotenuse is always the longest side. Angles must be strictly between 0° and 90° — at 0° or 90° the triangle degenerates.
Frequently asked questions
SOH CAH TOA is a mnemonic for the three primary trig ratios: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent. Knowing any two parts of one ratio lets you find the third, which in turn lets you solve for the unknown sides of a right triangle.
No — the SOH CAH TOA ratios apply only to right triangles. For non-right (oblique) triangles, you need the Law of Sines (a/sin A = b/sin B = c/sin C) or the Law of Cosines (c² = a² + b² − 2ab cos C). A dedicated oblique triangle calculator handles those cases.
The angle A refers to one of the two acute angles in a right triangle. All interior angles of any triangle sum to 180°, and one angle is already 90°, leaving only 90° shared between A and B. An angle of 0° or 90° would collapse the triangle to a line, making the calculation meaningless.
Also known as
TG we-Calculate Editorial Team. (2026). Trigonometry Calculator — Right Triangle Solver [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/trigonometry-calculator
TG we-Calculate Editorial Team. "Trigonometry Calculator — Right Triangle Solver." TG we-Calculate. 2026. https://we-calculate.com/calculator/trigonometry-calculator.
TG we-Calculate Editorial Team, "Trigonometry Calculator — Right Triangle Solver," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/trigonometry-calculator
@misc{wecalculate_trigonometry_calculator, title = {Trigonometry Calculator — Right Triangle Solver}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/trigonometry-calculator}}, year = {2026}, note = {TG we-Calculate} }
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