9 16 23 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 16   c = 23

Area: T = 53.666563146
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 16.95774262942° = 16°57'27″ = 0.29659629215 rad
Angle ∠ B = β = 31.232225881° = 31°13'56″ = 0.54551057491 rad
Angle ∠ C = γ = 131.8110314896° = 131°48'37″ = 2.3010523983 rad

Height: ha = 11.926569588
Height: hb = 6.70882039325
Height: hc = 4.66765766487

Median: ma = 19.29437813816
Median: mb = 15.52441746963
Median: mc = 6.02107972894

Inradius: r = 2.23660679775
Circumradius: R = 15.42988690447

Vertex coordinates: A[23; 0] B[0; 0] C[7.69656521739; 4.66765766487]
Centroid: CG[10.2321884058; 1.55655255496]
Coordinates of the circumscribed circle: U[11.5; -10.28659126965]
Coordinates of the inscribed circle: I[8; 2.23660679775]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.0432573706° = 163°2'33″ = 0.29659629215 rad
∠ B' = β' = 148.768774119° = 148°46'4″ = 0.54551057491 rad
∠ C' = γ' = 48.19896851042° = 48°11'23″ = 2.3010523983 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 = 9 ; ; b = 16 ; ; c = 23 ; ;

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

p = a+b+c = 9+16+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 * (24-9)(24-16)(24-23) } ; ; T = sqrt{ 2880 } = 53.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 53.67 }{ 9 } = 11.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 53.67 }{ 16 } = 6.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 53.67 }{ 23 } = 4.67 ; ;

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{ 9**2-16**2-23**2 }{ 2 * 16 * 23 } ) = 16° 57'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-9**2-23**2 }{ 2 * 9 * 23 } ) = 31° 13'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-9**2-16**2 }{ 2 * 16 * 9 } ) = 131° 48'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 53.67 }{ 24 } = 2.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 16° 57'27" } = 15.43 ; ;




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

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