Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 200   b = 190   c = 293.11

Area: T = 18840.93990778
Perimeter: p = 683.11
Semiperimeter: s = 341.555

Angle ∠ A = α = 42.58105003255° = 42°34'50″ = 0.74331699278 rad
Angle ∠ B = β = 400.0004885349° = 40°2″ = 0.69881402273 rad
Angle ∠ C = γ = 97.41990111395° = 97°25'8″ = 1.77002824984 rad

Height: ha = 188.4099390778
Height: hb = 198.3265674503
Height: hc = 128.5598828275

Median: ma = 225.8476709186
Median: mb = 232.2322073689
Median: mc = 128.7310850906

Inradius: r = 55.16222405698
Circumradius: R = 147.792226176

Vertex coordinates: A[293.11; 0] B[0; 0] C[153.2087792467; 128.5598828275]
Centroid: CG[148.7732597489; 42.85329427583]
Coordinates of the circumscribed circle: U[146.555; -19.08436215445]
Coordinates of the inscribed circle: I[151.555; 55.16222405698]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.4199499674° = 137°25'10″ = 0.74331699278 rad
∠ B' = β' = 1409.999511465° = 139°59'58″ = 0.69881402273 rad
∠ C' = γ' = 82.58109888605° = 82°34'52″ = 1.77002824984 rad

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How did we calculate this triangle?

a = 200 ; ; b = 190 ; ; c = 293.11 ; ;

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

p = a+b+c = 200+190+293.11 = 683.11 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 683.11 }{ 2 } = 341.56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 341.56 * (341.56-200)(341.56-190)(341.56-293.11) } ; ; T = sqrt{ 354980985.33 } = 18840.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18840.94 }{ 200 } = 188.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18840.94 }{ 190 } = 198.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18840.94 }{ 293.11 } = 128.56 ; ;

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{ 190**2+293.11**2-200**2 }{ 2 * 190 * 293.11 } ) = 42° 34'50" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 200**2+293.11**2-190**2 }{ 2 * 200 * 293.11 } ) = 40° 2" ; ; gamma = 180° - alpha - beta = 180° - 42° 34'50" - 40° 2" = 97° 25'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18840.94 }{ 341.56 } = 55.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 200 }{ 2 * sin 42° 34'50" } = 147.79 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 190**2+2 * 293.11**2 - 200**2 } }{ 2 } = 225.847 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 293.11**2+2 * 200**2 - 190**2 } }{ 2 } = 232.232 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 190**2+2 * 200**2 - 293.11**2 } }{ 2 } = 128.731 ; ;
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