Two Sides from Hypotenuse and Angle
The side opposite the angle is the hypotenuse times the sine; the adjacent side is the hypotenuse times the cosine. Half their product is the area.
Your numbers
Side a
50cm
Side b
86.6cm
Area
2,165.06cm²
Formula
Side a = Hypotenuse × sin(Angle (°)), Side b = Hypotenuse × cos(Angle (°))
At 45 degrees the two legs are equal and the area is at its largest. Push the angle to 0 or 90 and the triangle flattens away.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Hypotenuse (cm)The longest side of a right triangle, facing the right angle. | 100 | 0 and up |
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 30 | 0 ~ 90 |
Step by step
Quick reference table
Results when only Hypotenuse (cm) changes and everything else stays put.
| Hypotenuse (cm) | Side a (cm) | Side b (cm) | Area (cm²) |
|---|---|---|---|
| 50 | 25 | 43.3 | 541.27 |
| 75 | 37.5 | 64.95 | 1,217.85 |
| 100 | 50 | 86.6 | 2,165.06 |
| 150 | 75 | 129.9 | 4,871.39 |
| 200 | 100 | 173.21 | 8,660.25 |
What each result means
| Result | At default values |
|---|---|
| Side a (cm)The length of the first side. | 50 |
| Side b (cm)The length of the second side. | 86.6 |
| Area (cm²)The space a shape covers — length squared. | 2,165.06 |
Common mistakes
At 45 degrees the two legs are equal and the area is at its largest. Push the angle to 0 or 90 and the triangle flattens away.
Glossary
- Hypotenuse
- The longest side of a right triangle, facing the right angle.
- Angle (°)
- An angle in degrees; a full turn is 360°.
- Side a
- The length of the first side.
- Side b
- The length of the second side.
- Area
- The space a shape covers — length squared.
Frequently asked questions
Q. How is Two Sides from Hypotenuse and Angle calculated?
Side a = Hypotenuse × sin(Angle (°)), Side b = Hypotenuse × cos(Angle (°)) — The side opposite the angle is the hypotenuse times the sine; the adjacent side is the hypotenuse times the cosine. Half their product is the area.
Q. Can you walk through an example?
With Hypotenuse 100cm, Angle (°) 30°, the answer is Side a 50cm.
Q. What do I need to enter?
Enter Hypotenuse, Angle (°). The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Hypotenuse (cm) moves the answer to Hypotenuse (cm) 50 → Side a (cm) 25 and Hypotenuse (cm) 200 → Side a (cm) 100. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
At 45 degrees the two legs are equal and the area is at its largest. Push the angle to 0 or 90 and the triangle flattens away.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.