40 40 56.57 triangle

Obtuse isosceles triangle.

Sides: a = 40   b = 40   c = 56.57

Area: T = 8009.999998938
Perimeter: p = 136.57
Semiperimeter: s = 68.285

Angle ∠ A = α = 44.99985237384° = 44°59'55″ = 0.78553723978 rad
Angle ∠ B = β = 44.99985237384° = 44°59'55″ = 0.78553723978 rad
Angle ∠ C = γ = 90.00329525231° = 90°11″ = 1.5710847858 rad

Height: ha = 409.9999999469
Height: hb = 409.9999999469
Height: hc = 28.28435424761

Median: ma = 44.72222813595
Median: mb = 44.72222813595
Median: mc = 28.28435424761

Inradius: r = 11.71656037041
Circumradius: R = 28.28550000376

Vertex coordinates: A[56.57; 0] B[0; 0] C[28.285; 28.28435424761]
Centroid: CG[28.285; 9.4287847492]
Coordinates of the circumscribed circle: U[28.285; -0.00114575614]
Coordinates of the inscribed circle: I[28.285; 11.71656037041]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.0011476262° = 135°5″ = 0.78553723978 rad
∠ B' = β' = 135.0011476262° = 135°5″ = 0.78553723978 rad
∠ C' = γ' = 89.99770474769° = 89°59'49″ = 1.5710847858 rad

Calculate another triangle




How did we calculate this triangle?

a = 40 ; ; b = 40 ; ; c = 56.57 ; ;

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

p = a+b+c = 40+40+56.57 = 136.57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 136.57 }{ 2 } = 68.29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 68.29 * (68.29-40)(68.29-40)(68.29-56.57) } ; ; T = sqrt{ 640000 } = 800 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 800 }{ 40 } = 40 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 800 }{ 40 } = 40 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 800 }{ 56.57 } = 28.28 ; ;

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{ 40**2-40**2-56.57**2 }{ 2 * 40 * 56.57 } ) = 44° 59'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 40**2-40**2-56.57**2 }{ 2 * 40 * 56.57 } ) = 44° 59'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 56.57**2-40**2-40**2 }{ 2 * 40 * 40 } ) = 90° 11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 800 }{ 68.29 } = 11.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 40 }{ 2 * sin 44° 59'55" } = 28.29 ; ;




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

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