13 13 18 triangle

Acute isosceles triangle.

Sides: a = 13   b = 13   c = 18

Area: T = 84.42774836768
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 46.18769385396° = 46°11'13″ = 0.80661141489 rad
Angle ∠ B = β = 46.18769385396° = 46°11'13″ = 0.80661141489 rad
Angle ∠ C = γ = 87.62661229208° = 87°37'34″ = 1.52993643557 rad

Height: ha = 12.98988436426
Height: hb = 12.98988436426
Height: hc = 9.38108315196

Median: ma = 14.2921605928
Median: mb = 14.2921605928
Median: mc = 9.38108315196

Inradius: r = 3.83876128944
Circumradius: R = 9.0087730266

Vertex coordinates: A[18; 0] B[0; 0] C[9; 9.38108315196]
Centroid: CG[9; 3.12769438399]
Coordinates of the circumscribed circle: U[9; 0.37331012536]
Coordinates of the inscribed circle: I[9; 3.83876128944]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.813306146° = 133°48'47″ = 0.80661141489 rad
∠ B' = β' = 133.813306146° = 133°48'47″ = 0.80661141489 rad
∠ C' = γ' = 92.37438770792° = 92°22'26″ = 1.52993643557 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 = 13 ; ; c = 18 ; ;

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

p = a+b+c = 13+13+18 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-13)(22-13)(22-18) } ; ; T = sqrt{ 7128 } = 84.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 84.43 }{ 13 } = 12.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 84.43 }{ 13 } = 12.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 84.43 }{ 18 } = 9.38 ; ;

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**2-13**2-18**2 }{ 2 * 13 * 18 } ) = 46° 11'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-13**2-18**2 }{ 2 * 13 * 18 } ) = 46° 11'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-13**2-13**2 }{ 2 * 13 * 13 } ) = 87° 37'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 84.43 }{ 22 } = 3.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 46° 11'13" } = 9.01 ; ;




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

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