Two legs, a leg and the hypotenuse, or a leg and an angle — each is enough to determine everything else.
A right triangle already has one angle fixed at 90°, so any two further pieces of information determine it completely. Two sides, or one side and one acute angle, and everything else follows.
What does not work is two angles. Knowing both acute angles fixes the shape but not the size — you would have a family of similar triangles, all the same proportions at different scales. At least one length is always required.
With an angle A and a side, the three ratios do the work:
Given leg a = 3 and angle A = 30°, the hypotenuse is a ÷ sin(30°) = 6 and the other leg is a ÷ tan(30°) = 5.1962.
The angles of any triangle add to 180°, and one of them here is already 90°, so the other two must share the remaining 90° between them. Find one and you have the other by subtraction — no trigonometry needed for the second.
The area is simply ½ × a × b, using the two legs. They are perpendicular to each other, so one serves as the base and the other as the height with no extra work — the only triangle where that is true without construction.
No. The two acute angles determine the shape but not the size, giving infinitely many similar triangles. You need at least one side length.
Because the triangle already contains a 90° angle and the three must total 180°. Both remaining angles have to be acute, and they always sum to exactly 90°.
It depends on the angle you are working from. The opposite leg is the one not touching that angle; the adjacent leg is the one that does, excluding the hypotenuse. Swap the angle and the two swap roles.
In a right triangle you already do. The two legs are perpendicular, so area is ½ × leg a × leg b with no separate height needed.
If you know two sides and just want the third, the Pythagorean Theorem Calculator is the quicker route. For triangles without a right angle use the Triangle Calculator, and for the trigonometric functions directly, the Scientific Calculator.