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

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 = 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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 13.5**2-9.6**2-9.4**2 }{ 2 * 9.6 * 9.4 } ) = 90° 32'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9.6**2-13.5**2-9.4**2 }{ 2 * 13.5 * 9.4 } ) = 45° 19'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.4**2-13.5**2-9.6**2 }{ 2 * 9.6 * 13.5 } ) = 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 ; ;




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