# Right triangle calculator (c)

Please enter two properties of the right triangle

Use symbols: a, b, c, A, B, h, T, p, r, R

You have entered cathetus a and hypotenuse c.

## Right scalene triangle.

The lengths of the sides of the triangle:
a = 10
b = 11.18803398875
c = 15

Area: T = 55.90216994375
Perimeter: p = 36.18803398875
Semiperimeter: s = 18.09901699437

Angle ∠ A = α = 41.81103148958° = 41°48'37″ = 0.73297276562 rad
Angle ∠ B = β = 48.19896851042° = 48°11'23″ = 0.84110686706 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Altitude (height) to the side a: ha = 11.18803398875
Altitude (height) to the side b: hb = 10
Altitude (height) to the side c: hc = 7.4543559925

Median: ma = 12.24774487139
Median: mb = 11.45664392374
Median: mc = 7.5

Line segment ca = 8.33333333333
Line segment cb = 6.66766666667

Vertex coordinates: A[15; 0] B[0; 0] C[6.66766666667; 7.4543559925]
Centroid: CG[7.22222222222; 2.4854519975]
Coordinates of the circumscribed circle: U[7.5; 0]
Coordinates of the inscribed circle: I[6.91098300563; 3.09901699437]

Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 138.19896851042° = 138°11'23″ = 0.73297276562 rad
∠ B' = β' = 131.81103148958° = 131°48'37″ = 0.84110686706 rad
∠ C' = γ' = 90° = 1.57107963268 rad

## How did we calculate this triangle?

The calculation of the triangle has two phases. The first phase calculates all three sides of the triangle from the input parameters. The first phase is different for the different triangles query entered. The second phase calculates other triangle characteristics, such as angles, area, perimeter, heights, the center of gravity, circle radii, etc. Some input data also results in two to three correct triangle solutions (e.g., if the specified triangle area and two sides - typically resulting in both acute and obtuse) triangle).

### 2. From the cathetus a and hypotenuse c, we calculate cathetus b - Pythagorean theorem:

We know the lengths of all three sides of the triangle, so the triangle is uniquely specified. Next, we calculate another of its characteristics - the same procedure for calculating the triangle from the known three sides SSS.

### 4. Semiperimeter of the triangle

The semiperimeter of the triangle is half its perimeter. The semiperimeter frequently appears in formulas for triangles to be given a separate name. By the triangle inequality, the longest side length of a triangle is less than the semiperimeter.

### 7. Calculation of the inner angles of the triangle - basic use of sine function

An incircle of a triangle is a tangent circle to each side. An incircle center is called an incenter and has a radius named inradius. All triangles have an incenter, and it always lies inside the triangle. The incenter is the intersection of the three-angle bisectors. The product of a triangle's inradius and semiperimeter (half the perimeter) is its area.