Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 1.86   b = 2.78   c = 3.71

Area: T = 2.50439019468
Perimeter: p = 8.35
Semiperimeter: s = 4.175

Angle ∠ A = α = 29.0488121141° = 29°2'53″ = 0.50769853554 rad
Angle ∠ B = β = 46.52875750737° = 46°31'39″ = 0.8122059378 rad
Angle ∠ C = γ = 104.4244303785° = 104°25'27″ = 1.82325479202 rad

Height: ha = 2.69223676848
Height: hb = 1.80113683071
Height: hc = 1.35498123703

Median: ma = 3.14334614679
Median: mb = 2.58545212323
Median: mc = 1.46773019457

Inradius: r = 0.65997369933
Circumradius: R = 1.91553773198

Vertex coordinates: A[3.71; 0] B[0; 0] C[1.2879690027; 1.35498123703]
Centroid: CG[1.6633230009; 0.45499374568]
Coordinates of the circumscribed circle: U[1.855; -0.47771218683]
Coordinates of the inscribed circle: I[1.395; 0.65997369933]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.9521878859° = 150°57'7″ = 0.50769853554 rad
∠ B' = β' = 133.4722424926° = 133°28'21″ = 0.8122059378 rad
∠ C' = γ' = 75.57656962147° = 75°34'33″ = 1.82325479202 rad

Calculate another triangle




How did we calculate this triangle?

a = 1.86 ; ; b = 2.78 ; ; c = 3.71 ; ;

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

p = a+b+c = 1.86+2.78+3.71 = 8.35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8.35 }{ 2 } = 4.18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.18 * (4.18-1.86)(4.18-2.78)(4.18-3.71) } ; ; T = sqrt{ 6.27 } = 2.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.5 }{ 1.86 } = 2.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.5 }{ 2.78 } = 1.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.5 }{ 3.71 } = 1.35 ; ;

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{ 1.86**2-2.78**2-3.71**2 }{ 2 * 2.78 * 3.71 } ) = 29° 2'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.78**2-1.86**2-3.71**2 }{ 2 * 1.86 * 3.71 } ) = 46° 31'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.71**2-1.86**2-2.78**2 }{ 2 * 2.78 * 1.86 } ) = 104° 25'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.5 }{ 4.18 } = 0.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.86 }{ 2 * sin 29° 2'53" } = 1.92 ; ;




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

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