8 12 15 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 12   c = 15

Area: T = 47.81114787473
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 32.08991838633° = 32°5'21″ = 0.56600619127 rad
Angle ∠ B = β = 52.8311100344° = 52°49'52″ = 0.92220766485 rad
Angle ∠ C = γ = 95.08797157927° = 95°4'47″ = 1.65994540924 rad

Height: ha = 11.95328696868
Height: hb = 7.96985797912
Height: hc = 6.3754863833

Median: ma = 12.98107549857
Median: mb = 10.4166333328
Median: mc = 6.91101374805

Inradius: r = 2.73220844998
Circumradius: R = 7.53295725929

Vertex coordinates: A[15; 0] B[0; 0] C[4.83333333333; 6.3754863833]
Centroid: CG[6.61111111111; 2.1254954611]
Coordinates of the circumscribed circle: U[7.5; -0.66766809067]
Coordinates of the inscribed circle: I[5.5; 2.73220844998]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.9110816137° = 147°54'39″ = 0.56600619127 rad
∠ B' = β' = 127.1698899656° = 127°10'8″ = 0.92220766485 rad
∠ C' = γ' = 84.92202842073° = 84°55'13″ = 1.65994540924 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 = 15 ; ;

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

p = a+b+c = 8+12+15 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-8)(17.5-12)(17.5-15) } ; ; T = sqrt{ 2285.94 } = 47.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.81 }{ 8 } = 11.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.81 }{ 12 } = 7.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.81 }{ 15 } = 6.37 ; ;

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**2-15**2 }{ 2 * 12 * 15 } ) = 32° 5'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-8**2-15**2 }{ 2 * 8 * 15 } ) = 52° 49'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-8**2-12**2 }{ 2 * 12 * 8 } ) = 95° 4'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.81 }{ 17.5 } = 2.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 32° 5'21" } = 7.53 ; ;




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

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