# Right triangle calculator (a,r) - the result

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 inradius r.

### Right scalene triangle.

Sides: a = 14   b = 22.5   c = 26.5

Area: T = 157.5
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 31.89107918018° = 31°53'27″ = 0.5576599318 rad
Angle ∠ B = β = 58.10992081982° = 58°6'33″ = 1.01441970088 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 22.5
Height: hb = 14
Height: hc = 11.88767924528

Median: ma = 23.56437433359
Median: mb = 17.96600250557
Median: mc = 13.25

Line segment ca = 19.10437735849
Line segment cb = 7.39662264151

Inradius: r = 5
Circumradius: R = 13.25

Vertex coordinates: A[26.5; 0] B[0; 0] C[7.39662264151; 11.88767924528]
Centroid: CG[11.29987421384; 3.96222641509]
Coordinates of the circumscribed circle: U[13.25; -0]
Coordinates of the inscribed circle: I[9; 5]

Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 148.10992081982° = 148°6'33″ = 0.5576599318 rad
∠ B' = β' = 121.89107918019° = 121°53'27″ = 1.01441970088 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).

### 5. From the area S and hypotenuse c, we calculate height h:

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.

### 7. 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.

### 10. 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 the inradius and semiperimeter (half the perimeter) of a triangle is its area.