Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 4   b = 21   c = 24

Area: T = 29.64768801057
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 6.75662861124° = 6°45'23″ = 0.11879194379 rad
Angle ∠ B = β = 38.14442418483° = 38°8'39″ = 0.66657426109 rad
Angle ∠ C = γ = 135.0999472039° = 135°5'58″ = 2.35879306048 rad

Height: ha = 14.82334400528
Height: hb = 2.8243512391
Height: hc = 2.47105733421

Median: ma = 22.46110774452
Median: mb = 13.62990131704
Median: mc = 9.19223881554

Inradius: r = 1.2110076739
Circumradius: R = 177.0001024797

Vertex coordinates: A[24; 0] B[0; 0] C[3.14658333333; 2.47105733421]
Centroid: CG[9.04986111111; 0.82435244474]
Coordinates of the circumscribed circle: U[12; -12.04217392565]
Coordinates of the inscribed circle: I[3.5; 1.2110076739]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.2443713888° = 173°14'37″ = 0.11879194379 rad
∠ B' = β' = 141.8565758152° = 141°51'21″ = 0.66657426109 rad
∠ C' = γ' = 44.90105279607° = 44°54'2″ = 2.35879306048 rad

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How did we calculate this triangle?

a = 4 ; ; b = 21 ; ; c = 24 ; ;

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

p = a+b+c = 4+21+24 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-4)(24.5-21)(24.5-24) } ; ; T = sqrt{ 878.94 } = 29.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.65 }{ 4 } = 14.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.65 }{ 21 } = 2.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.65 }{ 24 } = 2.47 ; ;

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{ 21**2+24**2-4**2 }{ 2 * 21 * 24 } ) = 6° 45'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4**2+24**2-21**2 }{ 2 * 4 * 24 } ) = 38° 8'39" ; ; gamma = 180° - alpha - beta = 180° - 6° 45'23" - 38° 8'39" = 135° 5'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.65 }{ 24.5 } = 1.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4 }{ 2 * sin 6° 45'23" } = 17 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 21**2+2 * 24**2 - 4**2 } }{ 2 } = 22.461 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 4**2 - 21**2 } }{ 2 } = 13.629 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 21**2+2 * 4**2 - 24**2 } }{ 2 } = 9.192 ; ;
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