Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 37.3   b = 29.8   c = 50.93

Area: T = 550.17990892
Perimeter: p = 118.03
Semiperimeter: s = 59.015

Angle ∠ A = α = 46.47696989744° = 46°28'11″ = 0.81110492495 rad
Angle ∠ B = β = 35.39664519479° = 35°23'47″ = 0.618778463 rad
Angle ∠ C = γ = 98.13438490778° = 98°8'2″ = 1.71327587741 rad

Height: ha = 29.550021926
Height: hb = 36.92547710872
Height: hc = 21.60553048969

Median: ma = 37.325465606
Median: mb = 42.07881112932
Median: mc = 22.16330046474

Inradius: r = 9.32326991307
Circumradius: R = 25.72437749086

Vertex coordinates: A[50.93; 0] B[0; 0] C[30.40656047516; 21.60553048969]
Centroid: CG[27.11218682505; 7.2021768299]
Coordinates of the circumscribed circle: U[25.465; -3.64395563671]
Coordinates of the inscribed circle: I[29.215; 9.32326991307]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.5330301026° = 133°31'49″ = 0.81110492495 rad
∠ B' = β' = 144.6043548052° = 144°36'13″ = 0.618778463 rad
∠ C' = γ' = 81.86661509222° = 81°51'58″ = 1.71327587741 rad

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How did we calculate this triangle?

a = 37.3 ; ; b = 29.8 ; ; c = 50.93 ; ;

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

p = a+b+c = 37.3+29.8+50.93 = 118.03 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 118.03 }{ 2 } = 59.02 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 59.02 * (59.02-37.3)(59.02-29.8)(59.02-50.93) } ; ; T = sqrt{ 302697.03 } = 550.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 550.18 }{ 37.3 } = 29.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 550.18 }{ 29.8 } = 36.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 550.18 }{ 50.93 } = 21.61 ; ;

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{ 29.8**2+50.93**2-37.3**2 }{ 2 * 29.8 * 50.93 } ) = 46° 28'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 37.3**2+50.93**2-29.8**2 }{ 2 * 37.3 * 50.93 } ) = 35° 23'47" ; ; gamma = 180° - alpha - beta = 180° - 46° 28'11" - 35° 23'47" = 98° 8'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 550.18 }{ 59.02 } = 9.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 37.3 }{ 2 * sin 46° 28'11" } = 25.72 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 29.8**2+2 * 50.93**2 - 37.3**2 } }{ 2 } = 37.325 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 50.93**2+2 * 37.3**2 - 29.8**2 } }{ 2 } = 42.078 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 29.8**2+2 * 37.3**2 - 50.93**2 } }{ 2 } = 22.163 ; ;
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