Triangle calculator

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 69 b = 70 c = 41

Area: T = 1360.956554667
Perimeter: p = 180
Semiperimeter: s = 90

Angle ∠ A = α = 71.51439853209° = 71°30'50″ = 1.24881545051 rad
Angle ∠ B = β = 74.18548619223° = 74°11'5″ = 1.29547700957 rad
Angle ∠ C = γ = 34.30111527568° = 34°18'4″ = 0.59986680528 rad

Height: h_a = 39.44879868599
Height: h_b = 38.88444441904
Height: h_c = 66.38880754471

Median: m_a = 45.8288484592
Median: m_b = 44.67766158074
Median: m_c = 66.4109713145

Inradius: r = 15.12217282963
Circumradius: R = 36.37770147536

Vertex coordinates: A[41; 0] B[0; 0] C[18.80548780488; 66.38880754471]
Centroid: CG[19.93549593496; 22.12993584824]
Coordinates of the circumscribed circle: U[20.5; 30.05105774051]
Coordinates of the inscribed circle: I[20; 15.12217282963]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108.4866014679° = 108°29'10″ = 1.24881545051 rad
∠ B' = β' = 105.8155138078° = 105°48'55″ = 1.29547700957 rad
∠ C' = γ' = 145.6998847243° = 145°41'56″ = 0.59986680528 rad

Calculate another triangle

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.

$a = 69 ; ; b = 70 ; ; c = 41 ; ;$

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

$p = a+b+c = 69+70+41 = 180 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 180 }{ 2 } = 90 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 90 * (90-69)(90-70)(90-41) } ; ; T = sqrt{ 1852200 } = 1360.96 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1360.96 }{ 69 } = 39.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1360.96 }{ 70 } = 38.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1360.96 }{ 41 } = 66.39 ; ;$

5. Calculation of the inner angles of the triangle using a Law of Cosines

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 69**2-70**2-41**2 }{ 2 * 70 * 41 } ) = 71° 30'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 70**2-69**2-41**2 }{ 2 * 69 * 41 } ) = 74° 11'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 41**2-69**2-70**2 }{ 2 * 70 * 69 } ) = 34° 18'4" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 1360.96 }{ 90 } = 15.12 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 69 }{ 2 * sin 71° 30'50" } = 36.38 ; ;$

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

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