# Right triangle calculator (a,b) - 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 cathetus b.

### Right scalene triangle.

Sides: a = 15   b = 8   c = 17

Area: T = 60
Perimeter: p = 40
Semiperimeter: s = 20

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

Height: ha = 8
Height: hb = 15
Height: hc = 7.05988235294

Median: ma = 10.96658560997
Median: mb = 15.52441746963
Median: mc = 8.5

Line segment ca = 3.76547058824
Line segment cb = 13.23552941176

Inradius: r = 3
Circumradius: R = 8.5

Vertex coordinates: A[17; 0] B[0; 0] C[13.23552941176; 7.05988235294]
Centroid: CG[10.07884313725; 2.35329411765]
Coordinates of the circumscribed circle: U[8.5; -0]
Coordinates of the inscribed circle: I[12; 3]

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).

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

### 8. Inradius

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.

### 9. Circumradius

The circumcircle of a triangle is a circle that passes through all of the triangle's vertices, and the circumradius of a triangle is the radius of the triangle's circumcircle. The circumcenter (center of the circumcircle) is the point where the perpendicular bisectors of a triangle intersect.

### 10. Calculation of medians

A median of a triangle is a line segment joining a vertex to the opposite side's midpoint. Every triangle has three medians, and they all intersect each other at the triangle's centroid. The centroid divides each median into parts in the ratio of 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex. We use Apollonius's theorem to calculate the length of a median from the lengths of its side.

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See more information about triangles or more details on solving triangles.