Right Triangle Calculator: Find Missing Sides, Angles, Area and Altitude
Choose which two values you know. You get the third side, both acute angles, area, perimeter and the altitude to the hypotenuse, with a labelled drawing.
- Nothing you type is stored
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Sides
a = 3, b = 4, c = 5
- Angles
- A = 36.8699°, B = 53.1301°
- Area
- 6
- Perimeter
- 12
- Altitude to hypotenuse
- 2.4
Show working
- c = √(a² + b²) = √(9 + 16) = 5
- A = arctan(a/b) = 36.8699°
- B = 90° − A = 53.1301°
- Area = ½·a·b = 6
- h = ab/c = 2.4
How to use
- Choose what you know: two legs, a leg and the hypotenuse, or a side and angle A.
- Enter the values (angles in degrees).
- Read every side and angle; open “Show working”.
Good to know
Naming: the right angle is at C, so c is the hypotenuse. Leg a is opposite angle A and leg b is next to it. Then sin A = a/c, cos A = b/c, tan A = a/b, and A + B = 90°.
Pythagoras: c² = a² + b². From two legs, c = √(a² + b²); from a leg and the hypotenuse, the other leg is √(c² − a²). The hypotenuse must be the longest side.
Extras: area = ab/2, and the altitude from the right angle to the hypotenuse is h = ab/c. Use any one length unit; area comes in that unit squared.
Questions
What is the hypotenuse of a triangle with legs 3 and 4?
√(9 + 16) = 5. This is the famous 3-4-5 triangle.
How do I find the angle if I know two sides?
tan A = a/b, so A = arctan(a/b). For legs 3 and 4, A ≈ 36.87° and B ≈ 53.13°.
A ladder 10 m long makes 30° with the ground. How high does it reach?
Choose “hypotenuse + angle A”, c = 10, A = 30°: the height a = 10·sin 30° = 5 m.
Why does it say the hypotenuse is too short?
The hypotenuse is always the longest side, so it must be longer than the leg you entered.
Is my data stored or sent anywhere?
No. The calculation runs entirely in your browser; nothing you type leaves your device.