11 25 28 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 25   c = 28

Area: T = 137.1711425596
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 23.07439180656° = 23°4'26″ = 0.40327158416 rad
Angle ∠ B = β = 62.96443082106° = 62°57'52″ = 1.09989344895 rad
Angle ∠ C = γ = 93.96217737238° = 93°57'42″ = 1.64399423225 rad

Height: ha = 24.94402591992
Height: hb = 10.97437140477
Height: hc = 9.79879589711

Median: ma = 25.96663243452
Median: mb = 17.21219144781
Median: mc = 13.30441346957

Inradius: r = 4.28766070499
Circumradius: R = 14.03435349847

Vertex coordinates: A[28; 0] B[0; 0] C[5; 9.79879589711]
Centroid: CG[11; 3.26659863237]
Coordinates of the circumscribed circle: U[14; -0.97695896899]
Coordinates of the inscribed circle: I[7; 4.28766070499]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.9266081934° = 156°55'34″ = 0.40327158416 rad
∠ B' = β' = 117.0365691789° = 117°2'8″ = 1.09989344895 rad
∠ C' = γ' = 86.03882262762° = 86°2'18″ = 1.64399423225 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 = 11 ; ; b = 25 ; ; c = 28 ; ;

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

p = a+b+c = 11+25+28 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-11)(32-25)(32-28) } ; ; T = sqrt{ 18816 } = 137.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 137.17 }{ 11 } = 24.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 137.17 }{ 25 } = 10.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 137.17 }{ 28 } = 9.8 ; ;

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{ 25**2+28**2-11**2 }{ 2 * 25 * 28 } ) = 23° 4'26" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11**2+28**2-25**2 }{ 2 * 11 * 28 } ) = 62° 57'52" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 11**2+25**2-28**2 }{ 2 * 11 * 25 } ) = 93° 57'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 137.17 }{ 32 } = 4.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 23° 4'26" } = 14.03 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 28**2 - 11**2 } }{ 2 } = 25.966 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 11**2 - 25**2 } }{ 2 } = 17.212 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 11**2 - 28**2 } }{ 2 } = 13.304 ; ;
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.