Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 35   b = 33   c = 5.37

Area: T = 84.45876840785
Perimeter: p = 73.37
Semiperimeter: s = 36.685

Angle ∠ A = α = 107.6599518901° = 107°35'58″ = 1.87879658784 rad
Angle ∠ B = β = 63.99109800634° = 63°59'28″ = 1.11768532937 rad
Angle ∠ C = γ = 8.41095010356° = 8°24'34″ = 0.14767734815 rad

Height: ha = 4.82661533759
Height: hb = 5.11986475199
Height: hc = 31.45553758207

Median: ma = 15.89655481189
Median: mb = 18.83326432027
Median: mc = 33.9098564921

Inradius: r = 2.30222402638
Circumradius: R = 18.35993419227

Vertex coordinates: A[5.37; 0] B[0; 0] C[15.34879422719; 31.45553758207]
Centroid: CG[6.90659807573; 10.48551252736]
Coordinates of the circumscribed circle: U[2.685; 18.16219440269]
Coordinates of the inscribed circle: I[3.685; 2.30222402638]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 72.44004810989° = 72°24'2″ = 1.87879658784 rad
∠ B' = β' = 116.0099019937° = 116°32″ = 1.11768532937 rad
∠ C' = γ' = 171.5990498964° = 171°35'26″ = 0.14767734815 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 = 35+33+5.37 = 73.37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73.37 }{ 2 } = 36.69 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.69 * (36.69-35)(36.69-33)(36.69-5.37) } ; ; T = sqrt{ 7133.1 } = 84.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 84.46 }{ 35 } = 4.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 84.46 }{ 33 } = 5.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 84.46 }{ 5.37 } = 31.46 ; ;

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{ 33**2+5.37**2-35**2 }{ 2 * 33 * 5.37 } ) = 107° 35'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 35**2+5.37**2-33**2 }{ 2 * 35 * 5.37 } ) = 63° 59'28" ; ; gamma = 180° - alpha - beta = 180° - 107° 35'58" - 63° 59'28" = 8° 24'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 84.46 }{ 36.69 } = 2.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 35 }{ 2 * sin 107° 35'58" } = 18.36 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 5.37**2 - 35**2 } }{ 2 } = 15.896 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.37**2+2 * 35**2 - 33**2 } }{ 2 } = 18.833 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 35**2 - 5.37**2 } }{ 2 } = 33.909 ; ;
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