15 23 30 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 23   c = 30

Area: T = 168.5944187326
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 29.25437801209° = 29°15'14″ = 0.51105747818 rad
Angle ∠ B = β = 48.53304268964° = 48°31'50″ = 0.84770157367 rad
Angle ∠ C = γ = 102.2165792983° = 102°12'57″ = 1.78440021351 rad

Height: ha = 22.47992249768
Height: hb = 14.66603641153
Height: hc = 11.24396124884

Median: ma = 25.65663832213
Median: mb = 20.74224685127
Median: mc = 12.32988280059

Inradius: r = 4.95986525684
Circumradius: R = 15.34875042114

Vertex coordinates: A[30; 0] B[0; 0] C[9.93333333333; 11.24396124884]
Centroid: CG[13.31111111111; 3.74765374961]
Coordinates of the circumscribed circle: U[15; -3.24774429201]
Coordinates of the inscribed circle: I[11; 4.95986525684]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.7466219879° = 150°44'46″ = 0.51105747818 rad
∠ B' = β' = 131.4769573104° = 131°28'10″ = 0.84770157367 rad
∠ C' = γ' = 77.78442070173° = 77°47'3″ = 1.78440021351 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 = 23 ; ; c = 30 ; ;

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

p = a+b+c = 15+23+30 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-15)(34-23)(34-30) } ; ; T = sqrt{ 28424 } = 168.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 168.59 }{ 15 } = 22.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 168.59 }{ 23 } = 14.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 168.59 }{ 30 } = 11.24 ; ;

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**2-23**2-30**2 }{ 2 * 23 * 30 } ) = 29° 15'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-15**2-30**2 }{ 2 * 15 * 30 } ) = 48° 31'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-15**2-23**2 }{ 2 * 23 * 15 } ) = 102° 12'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 168.59 }{ 34 } = 4.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 29° 15'14" } = 15.35 ; ;




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