Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 3.28   b = 0.71   c = 3.2

Area: T = 1.13659943747
Perimeter: p = 7.19
Semiperimeter: s = 3.595

Angle ∠ A = α = 90.18803105192° = 90°10'49″ = 1.5743943339 rad
Angle ∠ B = β = 12.50113338863° = 12°30'5″ = 0.21881894372 rad
Angle ∠ C = γ = 77.31883555944° = 77°19'6″ = 1.34994598774 rad

Height: ha = 0.69326794968
Height: hb = 3.21999841541
Height: hc = 0.71099964842

Median: ma = 1.63878186713
Median: mb = 3.22107413743
Median: mc = 1.75224982168

Inradius: r = 0.3165992872
Circumradius: R = 1.64400081211

Vertex coordinates: A[3.2; 0] B[0; 0] C[3.2022234375; 0.71099964842]
Centroid: CG[2.1344078125; 0.23766654947]
Coordinates of the circumscribed circle: U[1.6; 0.36600369941]
Coordinates of the inscribed circle: I[2.885; 0.3165992872]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.82196894808° = 89°49'11″ = 1.5743943339 rad
∠ B' = β' = 167.4998666114° = 167°29'55″ = 0.21881894372 rad
∠ C' = γ' = 102.6821644406° = 102°40'54″ = 1.34994598774 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 = 3.28+0.71+3.2 = 7.19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7.19 }{ 2 } = 3.6 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.6 * (3.6-3.28)(3.6-0.71)(3.6-3.2) } ; ; T = sqrt{ 1.29 } = 1.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.14 }{ 3.28 } = 0.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.14 }{ 0.71 } = 3.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.14 }{ 3.2 } = 0.71 ; ;

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{ 0.71**2+3.2**2-3.28**2 }{ 2 * 0.71 * 3.2 } ) = 90° 10'49" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.28**2+3.2**2-0.71**2 }{ 2 * 3.28 * 3.2 } ) = 12° 30'5" ; ;
 gamma = 180° - alpha - beta = 180° - 90° 10'49" - 12° 30'5" = 77° 19'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.14 }{ 3.6 } = 0.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.28 }{ 2 * sin 90° 10'49" } = 1.64 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.71**2+2 * 3.2**2 - 3.28**2 } }{ 2 } = 1.638 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.2**2+2 * 3.28**2 - 0.71**2 } }{ 2 } = 3.221 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.71**2+2 * 3.28**2 - 3.2**2 } }{ 2 } = 1.752 ; ;
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