Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 12.65   b = 11.31   c = 5.66

Area: T = 32.0077295106
Perimeter: p = 29.62
Semiperimeter: s = 14.81

Angle ∠ A = α = 90.03216845016° = 90°1'54″ = 1.57113493257 rad
Angle ∠ B = β = 63.38993521124° = 63°23'22″ = 1.10663529051 rad
Angle ∠ C = γ = 26.5798963386° = 26°34'44″ = 0.46438904229 rad

Height: ha = 5.0660441914
Height: hb = 5.66599991346
Height: hc = 11.31099982707

Median: ma = 6.32222009617
Median: mb = 8.00331259518
Median: mc = 11.66602058301

Inradius: r = 2.1611194808
Circumradius: R = 6.32550009671

Vertex coordinates: A[5.66; 0] B[0; 0] C[5.6666254417; 11.31099982707]
Centroid: CG[3.7755418139; 3.77699994236]
Coordinates of the circumscribed circle: U[2.83; 5.65765658516]
Coordinates of the inscribed circle: I[3.5; 2.1611194808]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.96883154984° = 89°58'6″ = 1.57113493257 rad
∠ B' = β' = 116.6110647888° = 116°36'38″ = 1.10663529051 rad
∠ C' = γ' = 153.4211036614° = 153°25'16″ = 0.46438904229 rad

Calculate another triangle


How did we calculate this triangle?

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 12.65+11.31+5.66 = 29.62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29.62 }{ 2 } = 14.81 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.81 * (14.81-12.65)(14.81-11.31)(14.81-5.66) } ; ; T = sqrt{ 1024.47 } = 32.01 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32.01 }{ 12.65 } = 5.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32.01 }{ 11.31 } = 5.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32.01 }{ 5.66 } = 11.31 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 11.31**2+5.66**2-12.65**2 }{ 2 * 11.31 * 5.66 } ) = 90° 1'54" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.65**2+5.66**2-11.31**2 }{ 2 * 12.65 * 5.66 } ) = 63° 23'22" ; ; gamma = 180° - alpha - beta = 180° - 90° 1'54" - 63° 23'22" = 26° 34'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32.01 }{ 14.81 } = 2.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.65 }{ 2 * sin 90° 1'54" } = 6.33 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.31**2+2 * 5.66**2 - 12.65**2 } }{ 2 } = 6.322 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.66**2+2 * 12.65**2 - 11.31**2 } }{ 2 } = 8.003 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.31**2+2 * 12.65**2 - 5.66**2 } }{ 2 } = 11.66 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.