26.48 33 32 triangle

Acute scalene triangle.

Sides: a = 26.48   b = 33   c = 32

Area: T = 392.694403272
Perimeter: p = 91.48
Semiperimeter: s = 45.74

Angle ∠ A = α = 48.05108767629° = 48°3'3″ = 0.8398646008 rad
Angle ∠ B = β = 67.95112357012° = 67°57'4″ = 1.18659727938 rad
Angle ∠ C = γ = 63.99878875359° = 63°59'52″ = 1.11769738518 rad

Height: ha = 29.6659670145
Height: hb = 23.87996383467
Height: hc = 24.5433377045

Median: ma = 29.68550534781
Median: mb = 24.29770203935
Median: mc = 25.28803322763

Inradius: r = 8.58553527049
Circumradius: R = 17.80219511821

Vertex coordinates: A[32; 0] B[0; 0] C[9.9440475; 24.5433377045]
Centroid: CG[13.98801583333; 8.18111256817]
Coordinates of the circumscribed circle: U[16; 7.80444516714]
Coordinates of the inscribed circle: I[12.74; 8.58553527049]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.9499123237° = 131°56'57″ = 0.8398646008 rad
∠ B' = β' = 112.0498764299° = 112°2'56″ = 1.18659727938 rad
∠ C' = γ' = 116.0022112464° = 116°8″ = 1.11769738518 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 = 26.48 ; ; b = 33 ; ; c = 32 ; ;

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

p = a+b+c = 26.48+33+32 = 91.48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 91.48 }{ 2 } = 45.74 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 45.74 * (45.74-26.48)(45.74-33)(45.74-32) } ; ; T = sqrt{ 154208.6 } = 392.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 392.69 }{ 26.48 } = 29.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 392.69 }{ 33 } = 23.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 392.69 }{ 32 } = 24.54 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 33**2+32**2-26.48**2 }{ 2 * 33 * 32 } ) = 48° 3'3" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 26.48**2+32**2-33**2 }{ 2 * 26.48 * 32 } ) = 67° 57'4" ; ;
 gamma = 180° - alpha - beta = 180° - 48° 3'3" - 67° 57'4" = 63° 59'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 392.69 }{ 45.74 } = 8.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 26.48 }{ 2 * sin 48° 3'3" } = 17.8 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 32**2 - 26.48**2 } }{ 2 } = 29.685 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 32**2+2 * 26.48**2 - 33**2 } }{ 2 } = 24.297 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 26.48**2 - 32**2 } }{ 2 } = 25.28 ; ;
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