# Right triangle calculator (a,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 height h.

## Right scalene triangle.

The lengths of the sides of the triangle:
a = 17
b = 9.06766666667
c = 19.26766666667

Area: T = 77.06766666667
Perimeter: p = 45.33333333333
Semiperimeter: s = 22.66766666667

Angle ∠ A = α = 61.92875130641° = 61°55'39″ = 1.08108390005 rad
Angle ∠ B = β = 28.07224869359° = 28°4'21″ = 0.49899573263 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Altitude (height) to the side a: ha = 9.06766666667
Altitude (height) to the side b: hb = 17
Altitude (height) to the side c: hc = 8

Median: ma = 12.42879702464
Median: mb = 17.59440646558
Median: mc = 9.63333333333

Line segment ca = 4.26766666667
Line segment cb = 15

Inradius: r = 3.4
Circumradius: R = 9.63333333333

Vertex coordinates: A[19.26766666667; 0] B[0; 0] C[15; 8]
Centroid: CG[11.42222222222; 2.66766666667]
Coordinates of the circumscribed circle: U[9.63333333333; 0]
Coordinates of the inscribed circle: I[13.6; 3.4]

Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 118.07224869359° = 118°4'21″ = 1.08108390005 rad
∠ B' = β' = 151.92875130642° = 151°55'39″ = 0.49899573263 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).

### 3. 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.

### 5. 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.

### 8. 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.