13 26 30 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 26   c = 30

Area: T = 168.4439714735
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 25.58879901207° = 25°35'17″ = 0.44765946766 rad
Angle ∠ B = β = 59.74552125992° = 59°44'43″ = 1.04327506722 rad
Angle ∠ C = γ = 94.66767972801° = 94°40' = 1.65222473049 rad

Height: ha = 25.91438022669
Height: hb = 12.95769011335
Height: hc = 11.22993143157

Median: ma = 27.30884236088
Median: mb = 19.11880542943
Median: mc = 14.05334693226

Inradius: r = 4.8822310572
Circumradius: R = 15.05498948778

Vertex coordinates: A[30; 0] B[0; 0] C[6.55; 11.22993143157]
Centroid: CG[12.18333333333; 3.74331047719]
Coordinates of the circumscribed circle: U[15; -1.22444736957]
Coordinates of the inscribed circle: I[8.5; 4.8822310572]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.4122009879° = 154°24'43″ = 0.44765946766 rad
∠ B' = β' = 120.2554787401° = 120°15'17″ = 1.04327506722 rad
∠ C' = γ' = 85.33332027199° = 85°20' = 1.65222473049 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 = 26 ; ; c = 30 ; ;

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

p = a+b+c = 13+26+30 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-13)(34.5-26)(34.5-30) } ; ; T = sqrt{ 28371.94 } = 168.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 168.44 }{ 13 } = 25.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 168.44 }{ 26 } = 12.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 168.44 }{ 30 } = 11.23 ; ;

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**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 25° 35'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-13**2-30**2 }{ 2 * 13 * 30 } ) = 59° 44'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-13**2-26**2 }{ 2 * 26 * 13 } ) = 94° 40' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 168.44 }{ 34.5 } = 4.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 25° 35'17" } = 15.05 ; ;




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

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