15 19 30 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 19   c = 30

Area: T = 118.9298549979
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 24.66438107936° = 24°39'50″ = 0.43304647044 rad
Angle ∠ B = β = 31.90989763008° = 31°54'32″ = 0.55769166974 rad
Angle ∠ C = γ = 123.4277212906° = 123°25'38″ = 2.15442112518 rad

Height: ha = 15.85771399971
Height: hb = 12.51987947346
Height: hc = 7.92985699986

Median: ma = 23.96435139326
Median: mb = 21.73113138121
Median: mc = 8.24662112512

Inradius: r = 3.71765171868
Circumradius: R = 17.97329762146

Vertex coordinates: A[30; 0] B[0; 0] C[12.73333333333; 7.92985699986]
Centroid: CG[14.24444444444; 2.64328566662]
Coordinates of the circumscribed circle: U[15; -9.90109026866]
Coordinates of the inscribed circle: I[13; 3.71765171868]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.3366189206° = 155°20'10″ = 0.43304647044 rad
∠ B' = β' = 148.0911023699° = 148°5'28″ = 0.55769166974 rad
∠ C' = γ' = 56.57327870944° = 56°34'22″ = 2.15442112518 rad

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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 = 15 ; ; b = 19 ; ; c = 30 ; ;

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

p = a+b+c = 15+19+30 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-15)(32-19)(32-30) } ; ; T = sqrt{ 14144 } = 118.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 118.93 }{ 15 } = 15.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 118.93 }{ 19 } = 12.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 118.93 }{ 30 } = 7.93 ; ;

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{ 15**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 24° 39'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-15**2-30**2 }{ 2 * 15 * 30 } ) = 31° 54'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-15**2-19**2 }{ 2 * 19 * 15 } ) = 123° 25'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 118.93 }{ 32 } = 3.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 24° 39'50" } = 17.97 ; ;




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