8 12 16 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 12   c = 16

Area: T = 46.47658001545
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 46.56774634422° = 46°34'3″ = 0.81327555614 rad
Angle ∠ C = γ = 104.4787512186° = 104°28'39″ = 1.82334765819 rad

Height: ha = 11.61989500386
Height: hb = 7.74659666924
Height: hc = 5.80994750193

Median: ma = 13.56546599663
Median: mb = 11.13655287257
Median: mc = 6.32545553203

Inradius: r = 2.58219888975
Circumradius: R = 8.26223644719

Vertex coordinates: A[16; 0] B[0; 0] C[5.5; 5.80994750193]
Centroid: CG[7.16766666667; 1.93664916731]
Coordinates of the circumscribed circle: U[8; -2.0665591118]
Coordinates of the inscribed circle: I[6; 2.58219888975]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 133.4332536558° = 133°25'57″ = 0.81327555614 rad
∠ C' = γ' = 75.52224878141° = 75°31'21″ = 1.82334765819 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 = 8 ; ; b = 12 ; ; c = 16 ; ;

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

p = a+b+c = 8+12+16 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-8)(18-12)(18-16) } ; ; T = sqrt{ 2160 } = 46.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 46.48 }{ 8 } = 11.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 46.48 }{ 12 } = 7.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 46.48 }{ 16 } = 5.81 ; ;

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{ 8**2-12**2-16**2 }{ 2 * 12 * 16 } ) = 28° 57'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-8**2-16**2 }{ 2 * 8 * 16 } ) = 46° 34'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-8**2-12**2 }{ 2 * 12 * 8 } ) = 104° 28'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 46.48 }{ 18 } = 2.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 28° 57'18" } = 8.26 ; ;




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

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