Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 6.35   b = 3.18   c = 5.5

Area: T = 8.7454994311
Perimeter: p = 15.03
Semiperimeter: s = 7.515

Angle ∠ A = α = 89.93546454517° = 89°56'5″ = 1.57696556747 rad
Angle ∠ B = β = 30.05220861912° = 30°3'8″ = 0.52545078511 rad
Angle ∠ C = γ = 60.01332683571° = 60°48″ = 1.04774291277 rad

Height: ha = 2.75443289168
Height: hb = 5.5499996422
Height: hc = 3.18799979313

Median: ma = 3.17881401794
Median: mb = 5.72334735956
Median: mc = 4.2021779385

Inradius: r = 1.16436718977
Circumradius: R = 3.17550020655

Vertex coordinates: A[5.5; 0] B[0; 0] C[5.49663727273; 3.18799979313]
Centroid: CG[3.66554575758; 1.06599993104]
Coordinates of the circumscribed circle: U[2.75; 1.58768642399]
Coordinates of the inscribed circle: I[4.335; 1.16436718977]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.06553545483° = 90°3'55″ = 1.57696556747 rad
∠ B' = β' = 149.9487913809° = 149°56'52″ = 0.52545078511 rad
∠ C' = γ' = 119.9876731643° = 119°59'12″ = 1.04774291277 rad

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How did we calculate this triangle?

a = 6.35 ; ; b = 3.18 ; ; c = 5.5 ; ;

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

p = a+b+c = 6.35+3.18+5.5 = 15.03 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.03 }{ 2 } = 7.52 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.52 * (7.52-6.35)(7.52-3.18)(7.52-5.5) } ; ; T = sqrt{ 76.47 } = 8.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.74 }{ 6.35 } = 2.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.74 }{ 3.18 } = 5.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.74 }{ 5.5 } = 3.18 ; ;

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{ 3.18**2+5.5**2-6.35**2 }{ 2 * 3.18 * 5.5 } ) = 89° 56'5" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.35**2+5.5**2-3.18**2 }{ 2 * 6.35 * 5.5 } ) = 30° 3'8" ; ; gamma = 180° - alpha - beta = 180° - 89° 56'5" - 30° 3'8" = 60° 48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.74 }{ 7.52 } = 1.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.35 }{ 2 * sin 89° 56'5" } = 3.18 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.18**2+2 * 5.5**2 - 6.35**2 } }{ 2 } = 3.178 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.5**2+2 * 6.35**2 - 3.18**2 } }{ 2 } = 5.723 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.18**2+2 * 6.35**2 - 5.5**2 } }{ 2 } = 4.202 ; ;
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