12 15 25 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 15   c = 25

Area: T = 63.27771680782
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 19.72333084717° = 19°43'24″ = 0.34442366722 rad
Angle ∠ B = β = 24.95113010927° = 24°57'5″ = 0.43554823567 rad
Angle ∠ C = γ = 135.3255390436° = 135°19'31″ = 2.36218736246 rad

Height: ha = 10.54661946797
Height: hb = 8.43769557438
Height: hc = 5.06221734463

Median: ma = 19.72330829233
Median: mb = 18.1187670932
Median: mc = 5.31550729064

Inradius: r = 2.43437372338
Circumradius: R = 17.77989245974

Vertex coordinates: A[25; 0] B[0; 0] C[10.88; 5.06221734463]
Centroid: CG[11.96; 1.68773911488]
Coordinates of the circumscribed circle: U[12.5; -12.64327908248]
Coordinates of the inscribed circle: I[11; 2.43437372338]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.2776691528° = 160°16'36″ = 0.34442366722 rad
∠ B' = β' = 155.0498698907° = 155°2'55″ = 0.43554823567 rad
∠ C' = γ' = 44.67546095644° = 44°40'29″ = 2.36218736246 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 = 12 ; ; b = 15 ; ; c = 25 ; ;

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

p = a+b+c = 12+15+25 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-12)(26-15)(26-25) } ; ; T = sqrt{ 4004 } = 63.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 63.28 }{ 12 } = 10.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 63.28 }{ 15 } = 8.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 63.28 }{ 25 } = 5.06 ; ;

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{ 12**2-15**2-25**2 }{ 2 * 15 * 25 } ) = 19° 43'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-12**2-25**2 }{ 2 * 12 * 25 } ) = 24° 57'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-12**2-15**2 }{ 2 * 15 * 12 } ) = 135° 19'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 63.28 }{ 26 } = 2.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 19° 43'24" } = 17.78 ; ;




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

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