7 15 19 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 15   c = 19

Area: T = 47.78327113086
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 19.59218322609° = 19°35'31″ = 0.34219419795 rad
Angle ∠ B = β = 45.93438251762° = 45°56'2″ = 0.80216964874 rad
Angle ∠ C = γ = 114.4744342563° = 114°28'28″ = 1.99879541868 rad

Height: ha = 13.6522203231
Height: hb = 6.37110281745
Height: hc = 5.03297590851

Median: ma = 16.75655960801
Median: mb = 12.19663109177
Median: mc = 6.83773971656

Inradius: r = 2.33108639663
Circumradius: R = 10.43878756739

Vertex coordinates: A[19; 0] B[0; 0] C[4.86884210526; 5.03297590851]
Centroid: CG[7.95661403509; 1.67765863617]
Coordinates of the circumscribed circle: U[9.5; -4.32442627792]
Coordinates of the inscribed circle: I[5.5; 2.33108639663]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.4088167739° = 160°24'29″ = 0.34219419795 rad
∠ B' = β' = 134.0666174824° = 134°3'58″ = 0.80216964874 rad
∠ C' = γ' = 65.52656574372° = 65°31'32″ = 1.99879541868 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 = 15 ; ; c = 19 ; ;

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

p = a+b+c = 7+15+19 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-7)(20.5-15)(20.5-19) } ; ; T = sqrt{ 2283.19 } = 47.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.78 }{ 7 } = 13.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.78 }{ 15 } = 6.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.78 }{ 19 } = 5.03 ; ;

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**2-15**2-19**2 }{ 2 * 15 * 19 } ) = 19° 35'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-7**2-19**2 }{ 2 * 7 * 19 } ) = 45° 56'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-7**2-15**2 }{ 2 * 15 * 7 } ) = 114° 28'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.78 }{ 20.5 } = 2.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 19° 35'31" } = 10.44 ; ;




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

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