Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 105   b = 69.72   c = 113.32

Area: T = 3580.294350319
Perimeter: p = 288.04
Semiperimeter: s = 144.02

Angle ∠ A = α = 65.00325380454° = 65°9″ = 1.1354508311 rad
Angle ∠ B = β = 36.99989796535° = 36°59'56″ = 0.64657540148 rad
Angle ∠ C = γ = 77.99884823011° = 77°59'55″ = 1.36113303277 rad

Height: ha = 68.19660667275
Height: hb = 102.705491977
Height: hc = 63.18990840662

Median: ma = 78.07698430894
Median: mb = 103.5287733482
Median: mc = 68.79437758813

Inradius: r = 24.86596965921
Circumradius: R = 57.92661442714

Vertex coordinates: A[113.32; 0] B[0; 0] C[83.85878538652; 63.18990840662]
Centroid: CG[65.72659512884; 21.06330280221]
Coordinates of the circumscribed circle: U[56.66; 12.04550234601]
Coordinates of the inscribed circle: I[74.3; 24.86596965921]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.9977461955° = 114°59'51″ = 1.1354508311 rad
∠ B' = β' = 143.0011020347° = 143°4″ = 0.64657540148 rad
∠ C' = γ' = 102.0021517699° = 102°5″ = 1.36113303277 rad

Calculate another triangle




How did we calculate this triangle?

a = 105 ; ; b = 69.72 ; ; c = 113.32 ; ;

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

p = a+b+c = 105+69.72+113.32 = 288.04 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 288.04 }{ 2 } = 144.02 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 144.02 * (144.02-105)(144.02-69.72)(144.02-113.32) } ; ; T = sqrt{ 12818501.57 } = 3580.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3580.29 }{ 105 } = 68.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3580.29 }{ 69.72 } = 102.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3580.29 }{ 113.32 } = 63.19 ; ;

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{ 69.72**2+113.32**2-105**2 }{ 2 * 69.72 * 113.32 } ) = 65° 9" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 105**2+113.32**2-69.72**2 }{ 2 * 105 * 113.32 } ) = 36° 59'56" ; ; gamma = 180° - alpha - beta = 180° - 65° 9" - 36° 59'56" = 77° 59'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3580.29 }{ 144.02 } = 24.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 105 }{ 2 * sin 65° 9" } = 57.93 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 69.72**2+2 * 113.32**2 - 105**2 } }{ 2 } = 78.07 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 113.32**2+2 * 105**2 - 69.72**2 } }{ 2 } = 103.528 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 69.72**2+2 * 105**2 - 113.32**2 } }{ 2 } = 68.794 ; ;
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.