Trigonometry (Right Triangle) Calculator
Solve a right triangle's sides from one angle and the hypotenuse.
Formula
opposite = h × sin(θ), adjacent = h × cos(θ)
Inputs
- Known angle (°)
- Hypotenuse
What it does
Solves a right-angled triangle from one angle and the hypotenuse, giving the opposite and adjacent sides.
Where it's used
Slopes, ramps, roof pitches, force components and surveying.
How to use it
- Enter the known angle in degrees.
- Enter the hypotenuse (the longest side).
- Read the other two sides.
The formula explained
- opposite
- h × sin θ
- adjacent
- h × cos θ
- SOH-CAH-TOA
- sin = opp/hyp, cos = adj/hyp, tan = opp/adj
Worked example
A 5 m ladder at 35° to the ground.
Inputs:
- Known angle: 35 °
- Hypotenuse: 5
The calculator gives:
- Result: 2.86788 (opposite side)
- Adjacent side: 4.09576
- Other angle: 55°
Tips and common mistakes
- The other non-right angle is 90° − θ.
- The hypotenuse is always opposite the right angle.
- Check with Pythagoras: opp² + adj² = hyp².
Questions people ask
What do sin, cos and tan mean?
In a right triangle: sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse and tan θ = opposite / adjacent — often remembered as SOH-CAH-TOA.
How do I find an angle from two sides?
Use the inverse functions. A 5 m ladder reaching 4 m up a wall makes an angle of asin(4 / 5) ≈ 53.1° with the ground.
How can I check the answer?
With Pythagoras: opposite² + adjacent² = hypotenuse². For the example, 2.868² + 4.096² ≈ 25 = 5².
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