Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 13   b = 24   c = 30

Area: T = 151.1110679636
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 24.81989241279° = 24°49'8″ = 0.43331719428 rad
Angle ∠ B = β = 50.79883749279° = 50°47'54″ = 0.88765988972 rad
Angle ∠ C = γ = 104.3832700944° = 104°22'58″ = 1.82218218136 rad

Height: ha = 23.2487796867
Height: hb = 12.59325566363
Height: hc = 10.07440453091

Median: ma = 26.37770733782
Median: mb = 19.76110728454
Median: mc = 12.14549578015

Inradius: r = 4.51107665563
Circumradius: R = 15.48553383337

Vertex coordinates: A[30; 0] B[0; 0] C[8.21766666667; 10.07440453091]
Centroid: CG[12.73988888889; 3.3588015103]
Coordinates of the circumscribed circle: U[15; -3.84765183361]
Coordinates of the inscribed circle: I[9.5; 4.51107665563]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.1811075872° = 155°10'52″ = 0.43331719428 rad
∠ B' = β' = 129.2021625072° = 129°12'6″ = 0.88765988972 rad
∠ C' = γ' = 75.61772990558° = 75°37'2″ = 1.82218218136 rad

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How did we calculate this triangle?

a = 13 ; ; b = 24 ; ; c = 30 ; ;

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

p = a+b+c = 13+24+30 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-13)(33.5-24)(33.5-30) } ; ; T = sqrt{ 22834.44 } = 151.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 151.11 }{ 13 } = 23.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 151.11 }{ 24 } = 12.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 151.11 }{ 30 } = 10.07 ; ;

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**2-13**2 }{ 2 * 24 * 30 } ) = 24° 49'8" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13**2+30**2-24**2 }{ 2 * 13 * 30 } ) = 50° 47'54" ; ; gamma = 180° - alpha - beta = 180° - 24° 49'8" - 50° 47'54" = 104° 22'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 151.11 }{ 33.5 } = 4.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 13 }{ 2 * sin 24° 49'8" } = 15.49 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 30**2 - 13**2 } }{ 2 } = 26.377 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 13**2 - 24**2 } }{ 2 } = 19.761 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 13**2 - 30**2 } }{ 2 } = 12.145 ; ;
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