Trigonometry Calculator
Pick which two things you know about a right triangle — two legs, a leg and an angle, or the hypotenuse and an angle — and get every side, both acute angles, and the sin / cos / tan ratios at once.
Example: with What do you know? Two legs (a and b) · Leg a (opposite α) 3 · Leg b (two-legs mode) 4 · Hypotenuse c (hypotenuse mode) 10 · Angle α in degrees (angle modes) 30 → Sides a / b / c: 3.00 / 4.00 / 5.00.
Computed by the calculator below using its default values. Change any input to see your own numbers.
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Check it outSOHCAHTOA: how the trig ratios solve a triangle
Every right-triangle problem comes down to three ratios. SOH-CAH-TOA is the memory hook: sin α = opposite ÷ hypotenuse, cos α = adjacent ÷ hypotenuse, tan α = opposite ÷ adjacent. Know any two parts of the triangle and the ratios give you the rest.
Say a 10-ft ladder (the hypotenuse) leans against a wall at 30° from the ground. Height reached = 10 × sin 30° = 5 ft; distance from the wall = 10 × cos 30° ≈ 8.66 ft. Going the other way, two legs of 3 and 4 give tan α = 3 ÷ 4, so α = atan(0.75) ≈ 36.87° and the hypotenuse is 5. The second acute angle is always 90° minus the first, because a triangle’s angles total 180°. This tool works in degrees — the mode most geometry classes use — and reports each sine, cosine, and tangent to four decimals.
How it’s calculated
Two legs: c = √(a² + b²) and α = atan(a ÷ b). Leg + angle: c = a ÷ sin α and b = a ÷ tan α. Hypotenuse + angle: a = c × sin α and b = c × cos α. In every mode β = 90° − α, and the ratios are computed from the finished sides: sin α = a ÷ c, cos α = b ÷ c, tan α = a ÷ b. Angles are in degrees; α must be between 0° and 90°.
Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.
Common mistakes
- Leaving your calculator in radians — sin 30 in radian mode is −0.988, not 0.5. This page always works in degrees.
- Mixing up opposite and adjacent — the ratios are defined relative to the angle you picked, so label the sides from α’s point of view.
- Entering an angle of 90° or more — the second acute angle would vanish; α must stay between 0° and 90°.
Frequently asked questions
What does SOHCAHTOA stand for?
Sin = Opposite ÷ Hypotenuse, Cos = Adjacent ÷ Hypotenuse, Tan = Opposite ÷ Adjacent. It tells you which two sides each trig ratio compares.
How do I find sin, cos, and tan without knowing the angles?
From two sides. With legs 3 and 4 the hypotenuse is 5, so sin α = 3 ÷ 5 = 0.6, cos α = 4 ÷ 5 = 0.8, and tan α = 3 ÷ 4 = 0.75.
Does this trig calculator use degrees or radians?
Degrees. Multiply degrees by π ÷ 180 if you need radians — 30° is about 0.5236 rad.
How do I solve a right triangle with one side and one angle?
Use the ratio that links them. Given leg a and angle α: hypotenuse = a ÷ sin α and the other leg = a ÷ tan α. Given the hypotenuse: a = c × sin α, b = c × cos α.
Why do the two acute angles always add to 90 degrees?
All three angles of a triangle sum to 180°, and the right angle uses up 90° of that, leaving exactly 90° for the other two.