Right Triangle with legs 7 and 24
The hypotenuse, angles, area, and perimeter of a right triangle with legs 7 and 24. Adjust any field below to try your own numbers.
Leg A
7
Leg B
24
Hypotenuse
25
A right triangle with legs 7 and 24 has a hypotenuse of 25, angles of 16.260° and 73.740°, an area of 84, and a perimeter of 56.
Angle A
16.260°
Angle B
73.740°
Area
84
Perimeter
56
Altitude to Hypotenuse
6.72
What is a Right Triangle Calculator?
A right triangle calculator solves for every unknown side, angle, area, and perimeter of a triangle that contains a 90° angle, given just two known values. Because a right triangle has a fixed angle already, only two additional pieces of information — two sides, or one side and one acute angle — are needed to fully determine the entire shape.
Right triangles are the foundation of trigonometry: the sine, cosine, and tangent functions are all defined from the ratios between a right triangle's sides, which is why this calculator, in addition to solving side lengths, also reports both acute angles.
Scaled Versions of Your Triangle
Every row below scales your exact triangle's sides up or down by the same factor — the angles stay identical (similar triangles), while area scales with the square of the multiplier.
| Scale | Leg A | Leg B | Hypotenuse | Area |
|---|---|---|---|---|
| ×0.5 | 3.5 | 12.0 | 12.5 | 21.00 |
| ×1 (your triangle) | 7 | 24 | 25 | 84 |
| ×2 | 14 | 48 | 50 | 336 |
| ×3 | 21 | 72 | 75 | 756 |
| ×5 | 35 | 120 | 125 | 2100 |
| ×10 | 70 | 240 | 250 | 8400 |
How a Right Triangle Is Solved
Which formula applies depends on which two values you already know. With two sides, the Pythagorean theorem finds the third directly. With one side and one angle, trigonometric ratios (sine, cosine, tangent) find the rest.
The two acute angles in any right triangle always add up to 90° — if you know one, the other is simply 90° minus the first. This calculator solves six different two-known-value combinations automatically: any two sides, or any one side paired with angle A.
Special Right Triangles
Two right-triangle angle combinations show up so often in geometry and trigonometry that their side ratios are worth memorizing directly. A 45-45-90 triangle (an isosceles right triangle) always has legs in a 1 : 1 ratio and a hypotenuse of leg × √2. A 30-60-90 triangle always has sides in a fixed 1 : √3 : 2 ratio — the shortest leg, opposite the 30° angle, is always exactly half the hypotenuse.
These ratios let you solve a special right triangle instantly from a single known side, without needing the general trigonometric formulas at all — useful shortcuts that show up constantly in standardized tests and introductory trigonometry courses.
The Altitude to the Hypotenuse
Drawing a perpendicular line from the right angle down to the hypotenuse splits the original right triangle into two smaller right triangles, both similar to the original and to each other. This altitude has a clean formula — leg A times leg B, divided by the hypotenuse — and shows up in geometric mean relationships: the altitude is the geometric mean of the two segments it creates on the hypotenuse, a property used in several classic geometry proofs.
Example — Your Current Inputs
A right triangle with legs 7 and 24 has a hypotenuse of 25, angles of 16.260° and 73.740°, an area of 84, and a perimeter of 56.
Additional Example — A Ladder Against a Wall
A 13-foot ladder leans against a wall, reaching a point 12 feet up. Treating the wall, ground, and ladder as a right triangle (hypotenuse = 13, one leg = 12), the base distance from the wall is √(13² − 12²) = √25 = 5 feet. The angle between the ladder and the ground is arccos(5/13) ≈ 67.4° — a common real-world check for whether a ladder is at a safe climbing angle (generally recommended around 75°, following the "4-to-1" rule: 1 foot of base offset for every 4 feet of ladder height).
About These Parameters
- Leg A and Leg B
- The two sides forming the 90° angle. Angle A is defined as the angle opposite leg A (between leg B and the hypotenuse).
- Hypotenuse (C)
- The longest side, opposite the right angle. Can be entered directly instead of one of the legs.
- Angle A
- The acute angle opposite leg A, in degrees. Enter this together with any one side to solve the triangle using trigonometric ratios instead of two sides.
Frequently Asked Questions
What's the difference between this and the Pythagorean Theorem Calculator?
The Pythagorean Theorem Calculator only solves for a missing side from two known sides. This Right Triangle Calculator goes further — it also accepts a side and an angle, and reports both acute angles, area, perimeter, and the altitude to the hypotenuse, giving a complete picture of the triangle rather than just the missing side length.
Can I enter both angles instead of a side?
No — two angles alone (with the fixed 90°) only determine the triangle's shape, not its size, since infinitely many similarly-shaped right triangles share the same angles at different scales. You need at least one side length to pin down the actual dimensions.
Why do the two acute angles always add up to 90°?
The interior angles of any triangle always sum to 180°. A right triangle uses up 90° of that total on its right angle, leaving exactly 90° to be split between the remaining two angles — so they are always complementary to each other.
What is the "geometric mean" property of the altitude?
When you drop a perpendicular altitude from the right angle to the hypotenuse, it splits the hypotenuse into two segments. The altitude's length equals the geometric mean (square root of the product) of those two segment lengths — and each leg is the geometric mean of the hypotenuse and its adjacent segment. These "geometric mean" relationships are a classic tool for solving right-triangle problems in similarity-based geometry proofs.