Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 6.71   b = 6.32   c = 12.04

Area: T = 14.98876416243
Perimeter: p = 25.07
Semiperimeter: s = 12.535

Angle ∠ A = α = 23.19992957286° = 23°11'57″ = 0.40549040946 rad
Angle ∠ B = β = 21.77994314593° = 21°46'46″ = 0.38801227882 rad
Angle ∠ C = γ = 135.0211272812° = 135°1'17″ = 2.35765657708 rad

Height: ha = 4.46772553277
Height: hb = 4.74329245647
Height: hc = 2.49896414658

Median: ma = 9.01108809225
Median: mb = 9.22199376354
Median: mc = 2.49985695908

Inradius: r = 1.19656634722
Circumradius: R = 8.51767283285

Vertex coordinates: A[12.04; 0] B[0; 0] C[6.23110340532; 2.49896414658]
Centroid: CG[6.09903446844; 0.83298804886]
Coordinates of the circumscribed circle: U[6.02; -6.02444718791]
Coordinates of the inscribed circle: I[6.215; 1.19656634722]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.8010704271° = 156°48'3″ = 0.40549040946 rad
∠ B' = β' = 158.2210568541° = 158°13'14″ = 0.38801227882 rad
∠ C' = γ' = 44.97987271878° = 44°58'43″ = 2.35765657708 rad

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How did we calculate this triangle?

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

p = a+b+c = 6.71+6.32+12.04 = 25.07 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25.07 }{ 2 } = 12.54 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.54 * (12.54-6.71)(12.54-6.32)(12.54-12.04) } ; ; T = sqrt{ 224.63 } = 14.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.99 }{ 6.71 } = 4.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.99 }{ 6.32 } = 4.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.99 }{ 12.04 } = 2.49 ; ;

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{ 6.32**2+12.04**2-6.71**2 }{ 2 * 6.32 * 12.04 } ) = 23° 11'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.71**2+12.04**2-6.32**2 }{ 2 * 6.71 * 12.04 } ) = 21° 46'46" ; ; gamma = 180° - alpha - beta = 180° - 23° 11'57" - 21° 46'46" = 135° 1'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.99 }{ 12.54 } = 1.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.71 }{ 2 * sin 23° 11'57" } = 8.52 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.32**2+2 * 12.04**2 - 6.71**2 } }{ 2 } = 9.011 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.04**2+2 * 6.71**2 - 6.32**2 } }{ 2 } = 9.22 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.32**2+2 * 6.71**2 - 12.04**2 } }{ 2 } = 2.499 ; ;
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