15 22 28 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 22   c = 28

Area: T = 163.9311197458
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 32.15772086093° = 32°9'26″ = 0.56112491685 rad
Angle ∠ B = β = 51.31878125465° = 51°19'4″ = 0.89656647939 rad
Angle ∠ C = γ = 96.52549788441° = 96°31'30″ = 1.68546786912 rad

Height: ha = 21.85774929944
Height: hb = 14.90328361325
Height: hc = 11.7099371247

Median: ma = 24.03664306834
Median: mb = 19.58331560276
Median: mc = 12.5989678312

Inradius: r = 5.04440368449
Circumradius: R = 14.09112775348

Vertex coordinates: A[28; 0] B[0; 0] C[9.375; 11.7099371247]
Centroid: CG[12.45883333333; 3.9033123749]
Coordinates of the circumscribed circle: U[14; -1.60112815381]
Coordinates of the inscribed circle: I[10.5; 5.04440368449]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.8432791391° = 147°50'34″ = 0.56112491685 rad
∠ B' = β' = 128.6822187453° = 128°40'56″ = 0.89656647939 rad
∠ C' = γ' = 83.47550211559° = 83°28'30″ = 1.68546786912 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 = 22 ; ; c = 28 ; ;

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

p = a+b+c = 15+22+28 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-15)(32.5-22)(32.5-28) } ; ; T = sqrt{ 26873.44 } = 163.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 163.93 }{ 15 } = 21.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 163.93 }{ 22 } = 14.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 163.93 }{ 28 } = 11.71 ; ;

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**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 32° 9'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-15**2-28**2 }{ 2 * 15 * 28 } ) = 51° 19'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-15**2-22**2 }{ 2 * 22 * 15 } ) = 96° 31'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 163.93 }{ 32.5 } = 5.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 32° 9'26" } = 14.09 ; ;




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