Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 0.45   b = 90   c = 89.56

Area: T = 4.23549008311
Perimeter: p = 180.01
Semiperimeter: s = 90.005

Angle ∠ A = α = 0.06602059424° = 0°3'37″ = 0.00110507919 rad
Angle ∠ B = β = 167.8688368114° = 167°52'6″ = 2.93298557335 rad
Angle ∠ C = γ = 12.07114259434° = 12°4'17″ = 0.21106861281 rad

Height: ha = 18.82217814716
Height: hb = 0.09441089074
Height: hc = 0.09545712557

Median: ma = 89.78799876086
Median: mb = 44.56600499326
Median: mc = 45.22200492039

Inradius: r = 0.04770518397
Circumradius: R = 214.1244258417

Vertex coordinates: A[89.56; 0] B[0; 0] C[-0.44399503126; 0.09545712557]
Centroid: CG[29.70766832291; 0.03215237519]
Coordinates of the circumscribed circle: U[44.78; 209.3899468812]
Coordinates of the inscribed circle: I[0.005; 0.04770518397]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.9439794058° = 179°56'23″ = 0.00110507919 rad
∠ B' = β' = 12.13216318857° = 12°7'54″ = 2.93298557335 rad
∠ C' = γ' = 167.9298574057° = 167°55'43″ = 0.21106861281 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 = 0.45+90+89.56 = 180.01 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 180.01 }{ 2 } = 90.01 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 90.01 * (90.01-0.45)(90.01-90)(90.01-89.56) } ; ; T = sqrt{ 17.93 } = 4.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.23 }{ 0.45 } = 18.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.23 }{ 90 } = 0.09 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.23 }{ 89.56 } = 0.09 ; ;

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{ 90**2+89.56**2-0.45**2 }{ 2 * 90 * 89.56 } ) = 0° 3'37" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.45**2+89.56**2-90**2 }{ 2 * 0.45 * 89.56 } ) = 167° 52'6" ; ;
 gamma = 180° - alpha - beta = 180° - 0° 3'37" - 167° 52'6" = 12° 4'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.23 }{ 90.01 } = 0.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.45 }{ 2 * sin 0° 3'37" } = 214.12 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 89.56**2 - 0.45**2 } }{ 2 } = 89.78 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 89.56**2+2 * 0.45**2 - 90**2 } }{ 2 } = 44.56 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 0.45**2 - 89.56**2 } }{ 2 } = 45.22 ; ;
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