216 165 368 triangle

Obtuse scalene triangle.

Sides: a = 216   b = 165   c = 368

Area: T = 8990.612159975
Perimeter: p = 749
Semiperimeter: s = 374.5

Angle ∠ A = α = 17.22655165541° = 17°13'32″ = 0.30106419792 rad
Angle ∠ B = β = 13.07442203237° = 13°4'27″ = 0.22881881918 rad
Angle ∠ C = γ = 149.7700263122° = 149°42'1″ = 2.61327624826 rad

Height: ha = 83.24664037014
Height: hb = 108.97771103
Height: hc = 48.86220195638

Median: ma = 263.9332756588
Median: mb = 290.2310511835
Median: mc = 55.53882750902

Inradius: r = 24.00769735641
Circumradius: R = 364.77004393

Vertex coordinates: A[368; 0] B[0; 0] C[210.4010815217; 48.86220195638]
Centroid: CG[192.8800271739; 16.28773398546]
Coordinates of the circumscribed circle: U[184; -314.8821581591]
Coordinates of the inscribed circle: I[209.5; 24.00769735641]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.7744483446° = 162°46'28″ = 0.30106419792 rad
∠ B' = β' = 166.9265779676° = 166°55'33″ = 0.22881881918 rad
∠ C' = γ' = 30.32997368778° = 30°17'59″ = 2.61327624826 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 = 216 ; ; b = 165 ; ; c = 368 ; ;

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

p = a+b+c = 216+165+368 = 749 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 749 }{ 2 } = 374.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 374.5 * (374.5-216)(374.5-165)(374.5-368) } ; ; T = sqrt{ 80831096.94 } = 8990.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8990.61 }{ 216 } = 83.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8990.61 }{ 165 } = 108.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8990.61 }{ 368 } = 48.86 ; ;

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{ 165**2+368**2-216**2 }{ 2 * 165 * 368 } ) = 17° 13'32" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 216**2+368**2-165**2 }{ 2 * 216 * 368 } ) = 13° 4'27" ; ;
 gamma = 180° - alpha - beta = 180° - 17° 13'32" - 13° 4'27" = 149° 42'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8990.61 }{ 374.5 } = 24.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 216 }{ 2 * sin 17° 13'32" } = 364.7 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 165**2+2 * 368**2 - 216**2 } }{ 2 } = 263.933 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 368**2+2 * 216**2 - 165**2 } }{ 2 } = 290.231 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 165**2+2 * 216**2 - 368**2 } }{ 2 } = 55.538 ; ;
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