Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 2.66   b = 5.04   c = 5.7

Area: T = 6.70331992362
Perimeter: p = 13.4
Semiperimeter: s = 6.7

Angle ∠ A = α = 27.81881358398° = 27°49'5″ = 0.48655180622 rad
Angle ∠ B = β = 62.15545120744° = 62°9'16″ = 1.08548008807 rad
Angle ∠ C = γ = 90.02773520858° = 90°1'38″ = 1.57112737107 rad

Height: ha = 5.04399994257
Height: hb = 2.66599996969
Height: hc = 2.3521999732

Median: ma = 5.21331468424
Median: mb = 3.66550238744
Median: mc = 2.84988769717

Inradius: r = 11.0004774979
Circumradius: R = 2.85500003248

Vertex coordinates: A[5.7; 0] B[0; 0] C[1.24224561404; 2.3521999732]
Centroid: CG[2.31441520468; 0.78439999107]
Coordinates of the circumscribed circle: U[2.85; -0.00113605444]
Coordinates of the inscribed circle: I[1.66; 11.0004774979]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.182186416° = 152°10'55″ = 0.48655180622 rad
∠ B' = β' = 117.8455487926° = 117°50'44″ = 1.08548008807 rad
∠ C' = γ' = 89.97326479142° = 89°58'22″ = 1.57112737107 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 2.66 ; ; b = 5.04 ; ; c = 5.7 ; ;

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

p = a+b+c = 2.66+5.04+5.7 = 13.4 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13.4 }{ 2 } = 6.7 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.7 * (6.7-2.66)(6.7-5.04)(6.7-5.7) } ; ; T = sqrt{ 44.93 } = 6.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.7 }{ 2.66 } = 5.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.7 }{ 5.04 } = 2.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.7 }{ 5.7 } = 2.35 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 2.66**2-5.04**2-5.7**2 }{ 2 * 5.04 * 5.7 } ) = 27° 49'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.04**2-2.66**2-5.7**2 }{ 2 * 2.66 * 5.7 } ) = 62° 9'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.7**2-2.66**2-5.04**2 }{ 2 * 5.04 * 2.66 } ) = 90° 1'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.7 }{ 6.7 } = 1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.66 }{ 2 * sin 27° 49'5" } = 2.85 ; ;




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