Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 107   b = 77   c = 36.12

Area: T = 907.3332809081
Perimeter: p = 220.12
Semiperimeter: s = 110.06

Angle ∠ A = α = 139.2722183863° = 139°16'20″ = 2.43107581649 rad
Angle ∠ B = β = 28.0043914599° = 28°14″ = 0.48987605132 rad
Angle ∠ C = γ = 12.72439015379° = 12°43'26″ = 0.22220739755 rad

Height: ha = 16.95994917585
Height: hb = 23.56770859502
Height: hc = 50.24399119093

Median: ma = 27.47695686169
Median: mb = 69.96112549916
Median: mc = 91.4498545095

Inradius: r = 8.24439833644
Circumradius: R = 81.99765609701

Vertex coordinates: A[36.12; 0] B[0; 0] C[94.47219601329; 50.24399119093]
Centroid: CG[43.53106533776; 16.74766373031]
Coordinates of the circumscribed circle: U[18.06; 79.98329507515]
Coordinates of the inscribed circle: I[33.06; 8.24439833644]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 40.72878161369° = 40°43'40″ = 2.43107581649 rad
∠ B' = β' = 151.9966085401° = 151°59'46″ = 0.48987605132 rad
∠ C' = γ' = 167.2766098462° = 167°16'34″ = 0.22220739755 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 = 107+77+36.12 = 220.12 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 220.12 }{ 2 } = 110.06 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 110.06 * (110.06-107)(110.06-77)(110.06-36.12) } ; ; T = sqrt{ 823252.83 } = 907.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 907.33 }{ 107 } = 16.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 907.33 }{ 77 } = 23.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 907.33 }{ 36.12 } = 50.24 ; ;

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{ 77**2+36.12**2-107**2 }{ 2 * 77 * 36.12 } ) = 139° 16'20" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 107**2+36.12**2-77**2 }{ 2 * 107 * 36.12 } ) = 28° 14" ; ;
 gamma = 180° - alpha - beta = 180° - 139° 16'20" - 28° 14" = 12° 43'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 907.33 }{ 110.06 } = 8.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 107 }{ 2 * sin 139° 16'20" } = 82 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 77**2+2 * 36.12**2 - 107**2 } }{ 2 } = 27.47 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 36.12**2+2 * 107**2 - 77**2 } }{ 2 } = 69.961 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 77**2+2 * 107**2 - 36.12**2 } }{ 2 } = 91.449 ; ;
Calculate another triangle


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

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