4 24 27 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 24   c = 27

Area: T = 33.62994142084
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 5.95877163246° = 5°57'28″ = 0.10439817658 rad
Angle ∠ B = β = 38.51884730846° = 38°31'6″ = 0.67222741782 rad
Angle ∠ C = γ = 135.5243810591° = 135°31'26″ = 2.36553367097 rad

Height: ha = 16.81547071042
Height: hb = 2.8022451184
Height: hc = 2.49110677191

Median: ma = 25.46656631565
Median: mb = 15.11662164578
Median: mc = 10.66553645039

Inradius: r = 1.22328877894
Circumradius: R = 19.26988458974

Vertex coordinates: A[27; 0] B[0; 0] C[3.13296296296; 2.49110677191]
Centroid: CG[10.04332098765; 0.83303559064]
Coordinates of the circumscribed circle: U[13.5; -13.74991244163]
Coordinates of the inscribed circle: I[3.5; 1.22328877894]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.0422283675° = 174°2'32″ = 0.10439817658 rad
∠ B' = β' = 141.4821526915° = 141°28'54″ = 0.67222741782 rad
∠ C' = γ' = 44.47661894092° = 44°28'34″ = 2.36553367097 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 = 4 ; ; b = 24 ; ; c = 27 ; ;

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

p = a+b+c = 4+24+27 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-4)(27.5-24)(27.5-27) } ; ; T = sqrt{ 1130.94 } = 33.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.63 }{ 4 } = 16.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.63 }{ 24 } = 2.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.63 }{ 27 } = 2.49 ; ;

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{ 4**2-24**2-27**2 }{ 2 * 24 * 27 } ) = 5° 57'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-4**2-27**2 }{ 2 * 4 * 27 } ) = 38° 31'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-4**2-24**2 }{ 2 * 24 * 4 } ) = 135° 31'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.63 }{ 27.5 } = 1.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 5° 57'28" } = 19.27 ; ;




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