7 18 23 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 18   c = 23

Area: T = 49.47772675074
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 13.82987435443° = 13°49'43″ = 0.24113571063 rad
Angle ∠ B = β = 37.92546365774° = 37°55'29″ = 0.66219097759 rad
Angle ∠ C = γ = 128.2476619878° = 128°14'48″ = 2.23883257714 rad

Height: ha = 14.1366362145
Height: hb = 5.49774741675
Height: hc = 4.30223710876

Median: ma = 20.3533132437
Median: mb = 14.42222051019
Median: mc = 7.36554599313

Inradius: r = 2.06215528128
Circumradius: R = 14.64330883616

Vertex coordinates: A[23; 0] B[0; 0] C[5.52217391304; 4.30223710876]
Centroid: CG[9.50772463768; 1.43441236959]
Coordinates of the circumscribed circle: U[11.5; -9.06547689857]
Coordinates of the inscribed circle: I[6; 2.06215528128]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.1711256456° = 166°10'17″ = 0.24113571063 rad
∠ B' = β' = 142.0755363423° = 142°4'31″ = 0.66219097759 rad
∠ C' = γ' = 51.75333801217° = 51°45'12″ = 2.23883257714 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 = 7 ; ; b = 18 ; ; c = 23 ; ;

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

p = a+b+c = 7+18+23 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-7)(24-18)(24-23) } ; ; T = sqrt{ 2448 } = 49.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 49.48 }{ 7 } = 14.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 49.48 }{ 18 } = 5.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 49.48 }{ 23 } = 4.3 ; ;

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{ 7**2-18**2-23**2 }{ 2 * 18 * 23 } ) = 13° 49'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-7**2-23**2 }{ 2 * 7 * 23 } ) = 37° 55'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-7**2-18**2 }{ 2 * 18 * 7 } ) = 128° 14'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 49.48 }{ 24 } = 2.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 13° 49'43" } = 14.64 ; ;




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

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