Right Triangle Solver — Sides & Angles
Solve any right triangle given two sides or one side and one angle.
Solve a right triangle given one acute angle and one side
What Is the Right Triangle Solver — Sides & Angles?
The Right Triangle Solver finds all missing sides and angles of a right triangle given one angle (other than the 90° right angle) and one side length. Using the SOHCAHTOA trigonometric ratios and the Pythagorean theorem, it computes the complete triangle: all three sides and both acute angles.
Formula
How to Use
Enter angle A (in degrees) — one of the two acute angles of the right triangle. Then select which side you know (adjacent, opposite, or hypotenuse relative to angle A) and enter its length. Click Solve to get all three sides and angle B.
Example Calculation
Angle A = 30°, hypotenuse = 10 opposite = 10 × sin(30°) = 10 × 0.5 = 5 adjacent = 10 × cos(30°) = 10 × 0.866 = 8.660 Angle B = 90° − 30° = 60° Area = (1/2) × 5 × 8.660 = 21.651 sq units Verify: 5² + 8.66² = 25 + 75 = 100 = 10² ✓
Understanding Right Triangle — Sides & Angles
Right triangle trigonometry is one of the most practically useful areas of mathematics. Surveyors use it to measure heights of buildings and distances across rivers. Architects use it in structural design. Pilots and ship navigators use it for course corrections.
SOHCAHTOA is the entry point into trigonometry for most students. The three basic trig functions — sine, cosine, and tangent — along with their reciprocals (cosecant, secant, cotangent) form the foundation of all higher trigonometry.
Special right triangles (30-60-90 and 45-45-90) are worth memorizing because they produce exact values. The 30-60-90 triangle has sides 1 : √3 : 2, giving sin(30°) = 1/2, sin(60°) = √3/2. The 45-45-90 triangle has sides 1 : 1 : √2, giving sin(45°) = cos(45°) = √2/2.
Frequently Asked Questions
What is SOHCAHTOA?
SOHCAHTOA is a mnemonic for trig ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. It applies to right triangles.
Can I enter the angle in radians?
This tool accepts angles in degrees. Convert radians to degrees first using the Radians-Degrees Converter if needed.
What is the hypotenuse?
The hypotenuse is the longest side, always opposite the 90° right angle. It is always longer than either leg.
For non-right triangles, which tool should I use?
Use the Triangle Solver (Law of Sines & Cosines), which handles all triangle types: SSS, SAS, ASA, and AAS.
What is the 45-45-90 special triangle?
In a 45-45-90 triangle, the legs are equal and the hypotenuse is √2 times a leg. In a 30-60-90 triangle, the sides are in ratio 1 : √3 : 2.
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