Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 12.73   b = 8.06   c = 8.06

Area: T = 31.47332194685
Perimeter: p = 28.85
Semiperimeter: s = 14.425

Angle ∠ A = α = 104.3155386865° = 104°18'55″ = 1.82106469613 rad
Angle ∠ B = β = 37.84223065674° = 37°50'32″ = 0.66604728461 rad
Angle ∠ C = γ = 37.84223065674° = 37°50'32″ = 0.66604728461 rad

Height: ha = 4.94547320453
Height: hb = 7.8109731878
Height: hc = 7.8109731878

Median: ma = 4.94547320453
Median: mb = 9.86224211023
Median: mc = 9.86224211023

Inradius: r = 2.18218523028
Circumradius: R = 6.56989707152

Vertex coordinates: A[8.06; 0] B[0; 0] C[10.05329094293; 7.8109731878]
Centroid: CG[6.03876364764; 2.60332439593]
Coordinates of the circumscribed circle: U[4.03; 5.18875308439]
Coordinates of the inscribed circle: I[6.365; 2.18218523028]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 75.68546131348° = 75°41'5″ = 1.82106469613 rad
∠ B' = β' = 142.1587693433° = 142°9'28″ = 0.66604728461 rad
∠ C' = γ' = 142.1587693433° = 142°9'28″ = 0.66604728461 rad

Calculate another triangle




How did we calculate this triangle?

a = 12.73 ; ; b = 8.06 ; ; c = 8.06 ; ;

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

p = a+b+c = 12.73+8.06+8.06 = 28.85 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 28.85 }{ 2 } = 14.43 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.43 * (14.43-12.73)(14.43-8.06)(14.43-8.06) } ; ; T = sqrt{ 990.56 } = 31.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.47 }{ 12.73 } = 4.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.47 }{ 8.06 } = 7.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.47 }{ 8.06 } = 7.81 ; ;

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{ 8.06**2+8.06**2-12.73**2 }{ 2 * 8.06 * 8.06 } ) = 104° 18'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.73**2+8.06**2-8.06**2 }{ 2 * 12.73 * 8.06 } ) = 37° 50'32" ; ; gamma = 180° - alpha - beta = 180° - 104° 18'55" - 37° 50'32" = 37° 50'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.47 }{ 14.43 } = 2.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.73 }{ 2 * sin 104° 18'55" } = 6.57 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.06**2+2 * 8.06**2 - 12.73**2 } }{ 2 } = 4.945 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.06**2+2 * 12.73**2 - 8.06**2 } }{ 2 } = 9.862 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.06**2+2 * 12.73**2 - 8.06**2 } }{ 2 } = 9.862 ; ;
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.