Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 15   b = 16   c = 27

Area: T = 102.7422396312
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 28.40222819014° = 28°24'8″ = 0.49657133343 rad
Angle ∠ B = β = 30.48987955881° = 30°29'20″ = 0.5322129868 rad
Angle ∠ C = γ = 121.1098922511° = 121°6'32″ = 2.11437494514 rad

Height: ha = 13.6998986175
Height: hb = 12.8432799539
Height: hc = 7.6110547875

Median: ma = 20.88765985742
Median: mb = 20.32224014329
Median: mc = 7.63221687612

Inradius: r = 3.54328412521
Circumradius: R = 15.76875901881

Vertex coordinates: A[27; 0] B[0; 0] C[12.92659259259; 7.6110547875]
Centroid: CG[13.30986419753; 2.53768492917]
Coordinates of the circumscribed circle: U[13.5; -8.14765882639]
Coordinates of the inscribed circle: I[13; 3.54328412521]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.5987718099° = 151°35'52″ = 0.49657133343 rad
∠ B' = β' = 149.5111204412° = 149°30'40″ = 0.5322129868 rad
∠ C' = γ' = 58.89110774895° = 58°53'28″ = 2.11437494514 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 = 15+16+27 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-15)(29-16)(29-27) } ; ; T = sqrt{ 10556 } = 102.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 102.74 }{ 15 } = 13.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 102.74 }{ 16 } = 12.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 102.74 }{ 27 } = 7.61 ; ;

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{ 16**2+27**2-15**2 }{ 2 * 16 * 27 } ) = 28° 24'8" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 15**2+27**2-16**2 }{ 2 * 15 * 27 } ) = 30° 29'20" ; ;
 gamma = 180° - alpha - beta = 180° - 28° 24'8" - 30° 29'20" = 121° 6'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 102.74 }{ 29 } = 3.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 15 }{ 2 * sin 28° 24'8" } = 15.77 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 27**2 - 15**2 } }{ 2 } = 20.887 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 15**2 - 16**2 } }{ 2 } = 20.322 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 15**2 - 27**2 } }{ 2 } = 7.632 ; ;
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