13.5 9.6 9.4 triangle

Obtuse scalene triangle.

Sides: a = 13.5   b = 9.6   c = 9.4

Area: T = 45.11879270773
Perimeter: p = 32.5
Semiperimeter: s = 16.25

Angle ∠ A = α = 90.54992199499° = 90°32'57″ = 1.58803820232 rad
Angle ∠ B = β = 45.32327281209° = 45°19'22″ = 0.79110308317 rad
Angle ∠ C = γ = 44.12880519292° = 44°7'41″ = 0.77701797987 rad

Height: ha = 6.68441373448
Height: hb = 9.43995681411
Height: hc = 9.65995589526

Median: ma = 6.68656188943
Median: mb = 10.59655179203
Median: mc = 10.72991658576

Inradius: r = 2.77664878201
Circumradius: R = 6.75503101257

Vertex coordinates: A[9.4; 0] B[0; 0] C[9.49220212766; 9.65995589526]
Centroid: CG[6.29773404255; 3.21998529842]
Coordinates of the circumscribed circle: U[4.7; 4.84552746871]
Coordinates of the inscribed circle: I[6.65; 2.77664878201]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.45107800501° = 89°27'3″ = 1.58803820232 rad
∠ B' = β' = 134.6777271879° = 134°40'38″ = 0.79110308317 rad
∠ C' = γ' = 135.8721948071° = 135°52'19″ = 0.77701797987 rad

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How did we calculate this triangle?

a = 13.5 ; ; b = 9.6 ; ; c = 9.4 ; ;

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

p = a+b+c = 13.5+9.6+9.4 = 32.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32.5 }{ 2 } = 16.25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.25 * (16.25-13.5)(16.25-9.6)(16.25-9.4) } ; ; T = sqrt{ 2035.63 } = 45.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 45.12 }{ 13.5 } = 6.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 45.12 }{ 9.6 } = 9.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 45.12 }{ 9.4 } = 9.6 ; ;

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{ 9.6**2+9.4**2-13.5**2 }{ 2 * 9.6 * 9.4 } ) = 90° 32'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13.5**2+9.4**2-9.6**2 }{ 2 * 13.5 * 9.4 } ) = 45° 19'22" ; ; gamma = 180° - alpha - beta = 180° - 90° 32'57" - 45° 19'22" = 44° 7'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 45.12 }{ 16.25 } = 2.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 13.5 }{ 2 * sin 90° 32'57" } = 6.75 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.6**2+2 * 9.4**2 - 13.5**2 } }{ 2 } = 6.686 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.4**2+2 * 13.5**2 - 9.6**2 } }{ 2 } = 10.596 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.6**2+2 * 13.5**2 - 9.4**2 } }{ 2 } = 10.729 ; ;
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