Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 10.2   b = 6.71   c = 10.63

Area: T = 33.01217275943
Perimeter: p = 27.54
Semiperimeter: s = 13.77

Angle ∠ A = α = 67.76551731896° = 67°45'55″ = 1.18327253903 rad
Angle ∠ B = β = 37.51219160086° = 37°30'43″ = 0.65547064431 rad
Angle ∠ C = γ = 74.72329108019° = 74°43'22″ = 1.30441608202 rad

Height: ha = 6.47328877636
Height: hb = 9.84395611309
Height: hc = 6.21110494063

Median: ma = 7.28801442293
Median: mb = 9.8622171414
Median: mc = 6.80331481683

Inradius: r = 2.39773658384
Circumradius: R = 5.51096969548

Vertex coordinates: A[10.63; 0] B[0; 0] C[8.09109125118; 6.21110494063]
Centroid: CG[6.24403041706; 2.07703498021]
Coordinates of the circumscribed circle: U[5.315; 1.45217353526]
Coordinates of the inscribed circle: I[7.06; 2.39773658384]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.235482681° = 112°14'5″ = 1.18327253903 rad
∠ B' = β' = 142.4888083991° = 142°29'17″ = 0.65547064431 rad
∠ C' = γ' = 105.2777089198° = 105°16'38″ = 1.30441608202 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 = 10.2+6.71+10.63 = 27.54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27.54 }{ 2 } = 13.77 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.77 * (13.77-10.2)(13.77-6.71)(13.77-10.63) } ; ; T = sqrt{ 1089.77 } = 33.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.01 }{ 10.2 } = 6.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.01 }{ 6.71 } = 9.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.01 }{ 10.63 } = 6.21 ; ;

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{ 6.71**2+10.63**2-10.2**2 }{ 2 * 6.71 * 10.63 } ) = 67° 45'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10.2**2+10.63**2-6.71**2 }{ 2 * 10.2 * 10.63 } ) = 37° 30'43" ; ; gamma = 180° - alpha - beta = 180° - 67° 45'55" - 37° 30'43" = 74° 43'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.01 }{ 13.77 } = 2.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10.2 }{ 2 * sin 67° 45'55" } = 5.51 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.71**2+2 * 10.63**2 - 10.2**2 } }{ 2 } = 7.28 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.63**2+2 * 10.2**2 - 6.71**2 } }{ 2 } = 9.862 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.71**2+2 * 10.2**2 - 10.63**2 } }{ 2 } = 6.803 ; ;
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.