7 16 18 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 16   c = 18

Area: T = 55.79881854544
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 22.79882480997° = 22°47'54″ = 0.3987904493 rad
Angle ∠ B = β = 62.33659955038° = 62°20'10″ = 1.0887968364 rad
Angle ∠ C = γ = 94.86657563965° = 94°51'57″ = 1.65657197965 rad

Height: ha = 15.94223387012
Height: hb = 6.97547731818
Height: hc = 6.21997983838

Median: ma = 16.66658333125
Median: mb = 11.06879718106
Median: mc = 8.45657672626

Inradius: r = 2.72218627051
Circumradius: R = 9.03325517917

Vertex coordinates: A[18; 0] B[0; 0] C[3.25; 6.21997983838]
Centroid: CG[7.08333333333; 2.06765994613]
Coordinates of the circumscribed circle: U[9; -0.76661539466]
Coordinates of the inscribed circle: I[4.5; 2.72218627051]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.20217519° = 157°12'6″ = 0.3987904493 rad
∠ B' = β' = 117.6644004496° = 117°39'50″ = 1.0887968364 rad
∠ C' = γ' = 85.13442436035° = 85°8'3″ = 1.65657197965 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 = 7 ; ; b = 16 ; ; c = 18 ; ;

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

p = a+b+c = 7+16+18 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-7)(20.5-16)(20.5-18) } ; ; T = sqrt{ 3113.44 } = 55.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.8 }{ 7 } = 15.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.8 }{ 16 } = 6.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.8 }{ 18 } = 6.2 ; ;

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{ 7**2-16**2-18**2 }{ 2 * 16 * 18 } ) = 22° 47'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-7**2-18**2 }{ 2 * 7 * 18 } ) = 62° 20'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-7**2-16**2 }{ 2 * 16 * 7 } ) = 94° 51'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.8 }{ 20.5 } = 2.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 22° 47'54" } = 9.03 ; ;




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