5 27 28 triangle

Obtuse scalene triangle.

Sides: a = 5 b = 27 c = 28

Area: T = 67.0822039325
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 10.22221793906° = 10°13'20″ = 0.17884106871 rad
Angle ∠ B = β = 73.3988450401° = 73°23'54″ = 1.28110446254 rad
Angle ∠ C = γ = 96.37993702084° = 96°22'46″ = 1.68221373411 rad

Height: h_a = 26.833281573
Height: h_b = 4.969903995
Height: h_c = 4.79215742375

Median: m_a = 27.39106918496
Median: m_b = 14.90880515159
Median: m_c = 13.45436240471

Inradius: r = 2.23660679775
Circumradius: R = 14.08772282582

Vertex coordinates: A[28; 0] B[0; 0] C[1.42985714286; 4.79215742375]
Centroid: CG[9.81095238095; 1.59771914125]
Coordinates of the circumscribed circle: U[14; -1.56552475842]
Coordinates of the inscribed circle: I[3; 2.23660679775]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.7787820609° = 169°46'40″ = 0.17884106871 rad
∠ B' = β' = 106.6021549599° = 106°36'6″ = 1.28110446254 rad
∠ C' = γ' = 83.62106297916° = 83°37'14″ = 1.68221373411 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.

$a = 5 ; ; b = 27 ; ; c = 28 ; ;$

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

$p = a+b+c = 5+27+28 = 60 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-5)(30-27)(30-28) } ; ; T = sqrt{ 4500 } = 67.08 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 67.08 }{ 5 } = 26.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 67.08 }{ 27 } = 4.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 67.08 }{ 28 } = 4.79 ; ;$

5. Calculation of the inner angles of the triangle using a Law of Cosines

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 5**2-27**2-28**2 }{ 2 * 27 * 28 } ) = 10° 13'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-5**2-28**2 }{ 2 * 5 * 28 } ) = 73° 23'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-5**2-27**2 }{ 2 * 27 * 5 } ) = 96° 22'46" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 67.08 }{ 30 } = 2.24 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 10° 13'20" } = 14.09 ; ;$

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