Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 3.92   b = 49   c = 48

Area: T = 91.84397713926
Perimeter: p = 100.92
Semiperimeter: s = 50.46

Angle ∠ A = α = 4.47990771565° = 4°28'45″ = 0.07881746438 rad
Angle ∠ B = β = 102.5298547262° = 102°31'43″ = 1.7899460727 rad
Angle ∠ C = γ = 72.99223755811° = 72°59'33″ = 1.27439572827 rad

Height: ha = 46.85770262207
Height: hb = 3.74985620977
Height: hc = 3.82766571414

Median: ma = 48.46329590512
Median: mb = 23.65223402648
Median: mc = 25.14332535683

Inradius: r = 1.8220050959
Circumradius: R = 25.09876234484

Vertex coordinates: A[48; 0] B[0; 0] C[-0.855035; 3.82766571414]
Centroid: CG[15.717655; 1.27655523805]
Coordinates of the circumscribed circle: U[24; 7.34110287262]
Coordinates of the inscribed circle: I[1.46; 1.8220050959]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.5210922844° = 175°31'15″ = 0.07881746438 rad
∠ B' = β' = 77.47114527376° = 77°28'17″ = 1.7899460727 rad
∠ C' = γ' = 107.0087624419° = 107°27″ = 1.27439572827 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 = 3.92+49+48 = 100.92 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 100.92 }{ 2 } = 50.46 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 50.46 * (50.46-3.92)(50.46-49)(50.46-48) } ; ; T = sqrt{ 8434.54 } = 91.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 91.84 }{ 3.92 } = 46.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 91.84 }{ 49 } = 3.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 91.84 }{ 48 } = 3.83 ; ;

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{ 49**2+48**2-3.92**2 }{ 2 * 49 * 48 } ) = 4° 28'45" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.92**2+48**2-49**2 }{ 2 * 3.92 * 48 } ) = 102° 31'43" ; ;
 gamma = 180° - alpha - beta = 180° - 4° 28'45" - 102° 31'43" = 72° 59'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 91.84 }{ 50.46 } = 1.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.92 }{ 2 * sin 4° 28'45" } = 25.1 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 49**2+2 * 48**2 - 3.92**2 } }{ 2 } = 48.463 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 48**2+2 * 3.92**2 - 49**2 } }{ 2 } = 23.652 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 49**2+2 * 3.92**2 - 48**2 } }{ 2 } = 25.143 ; ;
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