Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 8   b = 19   c = 25

Area: T = 57.2366352085
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 13.94552833377° = 13°56'43″ = 0.24333911094 rad
Angle ∠ B = β = 34.91552062474° = 34°54'55″ = 0.6099385308 rad
Angle ∠ C = γ = 131.1439510415° = 131°8'22″ = 2.28988162362 rad

Height: ha = 14.30990880213
Height: hb = 6.02548791668
Height: hc = 4.57989081668

Median: ma = 21.84403296678
Median: mb = 15.94552187191
Median: mc = 7.5

Inradius: r = 2.20113981571
Circumradius: R = 16.59878432481

Vertex coordinates: A[25; 0] B[0; 0] C[6.56; 4.57989081668]
Centroid: CG[10.52; 1.52663027223]
Coordinates of the circumscribed circle: U[12.5; -10.92196337159]
Coordinates of the inscribed circle: I[7; 2.20113981571]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.0554716662° = 166°3'17″ = 0.24333911094 rad
∠ B' = β' = 145.0854793753° = 145°5'5″ = 0.6099385308 rad
∠ C' = γ' = 48.86604895851° = 48°51'38″ = 2.28988162362 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 = 8+19+25 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-8)(26-19)(26-25) } ; ; T = sqrt{ 3276 } = 57.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 57.24 }{ 8 } = 14.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 57.24 }{ 19 } = 6.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 57.24 }{ 25 } = 4.58 ; ;

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{ 19**2+25**2-8**2 }{ 2 * 19 * 25 } ) = 13° 56'43" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8**2+25**2-19**2 }{ 2 * 8 * 25 } ) = 34° 54'55" ; ; gamma = 180° - alpha - beta = 180° - 13° 56'43" - 34° 54'55" = 131° 8'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 57.24 }{ 26 } = 2.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8 }{ 2 * sin 13° 56'43" } = 16.6 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 25**2 - 8**2 } }{ 2 } = 21.84 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 8**2 - 19**2 } }{ 2 } = 15.945 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 8**2 - 25**2 } }{ 2 } = 7.5 ; ;
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.