13 16 28 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 16   c = 28

Area: T = 52.54546238925
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 13.56765254723° = 13°34' = 0.23767805375 rad
Angle ∠ B = β = 16.78105453515° = 16°46'50″ = 0.29328757667 rad
Angle ∠ C = γ = 149.6532929176° = 149°39'11″ = 2.61219363494 rad

Height: ha = 8.08437882911
Height: hb = 6.56880779866
Height: hc = 3.75331874209

Median: ma = 21.85774929944
Median: mb = 20.31100960116
Median: mc = 4.06220192023

Inradius: r = 1.84436710138
Circumradius: R = 27.71097806044

Vertex coordinates: A[28; 0] B[0; 0] C[12.44664285714; 3.75331874209]
Centroid: CG[13.48221428571; 1.25110624736]
Coordinates of the circumscribed circle: U[14; -23.91330077812]
Coordinates of the inscribed circle: I[12.5; 1.84436710138]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.4333474528° = 166°26' = 0.23767805375 rad
∠ B' = β' = 163.2199454648° = 163°13'10″ = 0.29328757667 rad
∠ C' = γ' = 30.34770708239° = 30°20'49″ = 2.61219363494 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 = 13 ; ; b = 16 ; ; c = 28 ; ;

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

p = a+b+c = 13+16+28 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-13)(28.5-16)(28.5-28) } ; ; T = sqrt{ 2760.94 } = 52.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.54 }{ 13 } = 8.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.54 }{ 16 } = 6.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.54 }{ 28 } = 3.75 ; ;

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{ 13**2-16**2-28**2 }{ 2 * 16 * 28 } ) = 13° 34' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-13**2-28**2 }{ 2 * 13 * 28 } ) = 16° 46'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-13**2-16**2 }{ 2 * 16 * 13 } ) = 149° 39'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.54 }{ 28.5 } = 1.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 13° 34' } = 27.71 ; ;




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

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