Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 5.6   b = 3.9   c = 7.43

Area: T = 10.70444993519
Perimeter: p = 16.93
Semiperimeter: s = 8.465

Angle ∠ A = α = 47.63216152034° = 47°37'54″ = 0.83113285133 rad
Angle ∠ B = β = 30.96767424254° = 30°58' = 0.54404716139 rad
Angle ∠ C = γ = 101.4021642371° = 101°24'6″ = 1.77697925263 rad

Height: ha = 3.82330354828
Height: hb = 5.48994868471
Height: hc = 2.88114264743

Median: ma = 5.23113908285
Median: mb = 6.28333072502
Median: mc = 3.08795738342

Inradius: r = 1.26545598762
Circumradius: R = 3.79897895704

Vertex coordinates: A[7.43; 0] B[0; 0] C[4.80218102288; 2.88114264743]
Centroid: CG[4.07772700763; 0.96604754914]
Coordinates of the circumscribed circle: U[3.715; -0.74991862171]
Coordinates of the inscribed circle: I[4.565; 1.26545598762]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.3688384797° = 132°22'6″ = 0.83113285133 rad
∠ B' = β' = 149.0333257575° = 149°2' = 0.54404716139 rad
∠ C' = γ' = 78.59883576288° = 78°35'54″ = 1.77697925263 rad

Calculate another triangle




How did we calculate this triangle?

a = 5.6 ; ; b = 3.9 ; ; c = 7.43 ; ;

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

p = a+b+c = 5.6+3.9+7.43 = 16.93 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.93 }{ 2 } = 8.47 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.47 * (8.47-5.6)(8.47-3.9)(8.47-7.43) } ; ; T = sqrt{ 114.59 } = 10.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.7 }{ 5.6 } = 3.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.7 }{ 3.9 } = 5.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.7 }{ 7.43 } = 2.88 ; ;

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{ 3.9**2+7.43**2-5.6**2 }{ 2 * 3.9 * 7.43 } ) = 47° 37'54" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.6**2+7.43**2-3.9**2 }{ 2 * 5.6 * 7.43 } ) = 30° 58' ; ; gamma = 180° - alpha - beta = 180° - 47° 37'54" - 30° 58' = 101° 24'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.7 }{ 8.47 } = 1.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.6 }{ 2 * sin 47° 37'54" } = 3.79 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.9**2+2 * 7.43**2 - 5.6**2 } }{ 2 } = 5.231 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.43**2+2 * 5.6**2 - 3.9**2 } }{ 2 } = 6.283 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.9**2+2 * 5.6**2 - 7.43**2 } }{ 2 } = 3.08 ; ;
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.