Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 15   b = 24   c = 30

Area: T = 178.2990318021
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 29.68662952314° = 29°41'11″ = 0.51881235945 rad
Angle ∠ B = β = 52.41104970351° = 52°24'38″ = 0.91547357359 rad
Angle ∠ C = γ = 97.90332077335° = 97°54'12″ = 1.70987333232 rad

Height: ha = 23.77220424028
Height: hb = 14.85875265017
Height: hc = 11.88660212014

Median: ma = 26.11103427783
Median: mb = 20.45772725455
Median: mc = 13.24876412995

Inradius: r = 5.1687835305
Circumradius: R = 15.14438397215

Vertex coordinates: A[30; 0] B[0; 0] C[9.15; 11.88660212014]
Centroid: CG[13.05; 3.96220070671]
Coordinates of the circumscribed circle: U[15; -2.08222779617]
Coordinates of the inscribed circle: I[10.5; 5.1687835305]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.3143704769° = 150°18'49″ = 0.51881235945 rad
∠ B' = β' = 127.5989502965° = 127°35'22″ = 0.91547357359 rad
∠ C' = γ' = 82.09767922665° = 82°5'48″ = 1.70987333232 rad

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How did we calculate this triangle?

a = 15 ; ; b = 24 ; ; c = 30 ; ;

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

p = a+b+c = 15+24+30 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-15)(34.5-24)(34.5-30) } ; ; T = sqrt{ 31787.44 } = 178.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 178.29 }{ 15 } = 23.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 178.29 }{ 24 } = 14.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 178.29 }{ 30 } = 11.89 ; ;

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{ 24**2+30**2-15**2 }{ 2 * 24 * 30 } ) = 29° 41'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 15**2+30**2-24**2 }{ 2 * 15 * 30 } ) = 52° 24'38" ; ; gamma = 180° - alpha - beta = 180° - 29° 41'11" - 52° 24'38" = 97° 54'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 178.29 }{ 34.5 } = 5.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 15 }{ 2 * sin 29° 41'11" } = 15.14 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 30**2 - 15**2 } }{ 2 } = 26.11 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 15**2 - 24**2 } }{ 2 } = 20.457 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 15**2 - 30**2 } }{ 2 } = 13.248 ; ;
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