Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 3.61   b = 7.07   c = 6.4

Area: T = 11.50884795156
Perimeter: p = 17.08
Semiperimeter: s = 8.54

Angle ∠ A = α = 30.57662486946° = 30°34'35″ = 0.53436562126 rad
Angle ∠ B = β = 85.02550085349° = 85°1'30″ = 1.48439663455 rad
Angle ∠ C = γ = 64.39987427705° = 64°23'55″ = 1.12439700955 rad

Height: ha = 6.37658889283
Height: hb = 3.25655811925
Height: hc = 3.59663998486

Median: ma = 6.49772628852
Median: mb = 3.80878635742
Median: mc = 4.61217783988

Inradius: r = 1.3487597133
Circumradius: R = 3.54883679616

Vertex coordinates: A[6.4; 0] B[0; 0] C[0.31330625; 3.59663998486]
Centroid: CG[2.23876875; 1.19987999495]
Coordinates of the circumscribed circle: U[3.2; 1.5333269445]
Coordinates of the inscribed circle: I[1.47; 1.3487597133]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.4243751305° = 149°25'26″ = 0.53436562126 rad
∠ B' = β' = 94.97549914651° = 94°58'30″ = 1.48439663455 rad
∠ C' = γ' = 115.601125723° = 115°36'5″ = 1.12439700955 rad

Calculate another triangle




How did we calculate this triangle?

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

p = a+b+c = 3.61+7.07+6.4 = 17.08 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.08 }{ 2 } = 8.54 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.54 * (8.54-3.61)(8.54-7.07)(8.54-6.4) } ; ; T = sqrt{ 132.45 } = 11.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.51 }{ 3.61 } = 6.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.51 }{ 7.07 } = 3.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.51 }{ 6.4 } = 3.6 ; ;

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{ 7.07**2+6.4**2-3.61**2 }{ 2 * 7.07 * 6.4 } ) = 30° 34'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.61**2+6.4**2-7.07**2 }{ 2 * 3.61 * 6.4 } ) = 85° 1'30" ; ; gamma = 180° - alpha - beta = 180° - 30° 34'35" - 85° 1'30" = 64° 23'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.51 }{ 8.54 } = 1.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.61 }{ 2 * sin 30° 34'35" } = 3.55 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 6.4**2 - 3.61**2 } }{ 2 } = 6.497 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.4**2+2 * 3.61**2 - 7.07**2 } }{ 2 } = 3.808 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 3.61**2 - 6.4**2 } }{ 2 } = 4.612 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.