10 12 16 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 12   c = 16

Area: T = 59.92549530663
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 38.62548328731° = 38°37'29″ = 0.67441305067 rad
Angle ∠ B = β = 48.50991831443° = 48°30'33″ = 0.84766449633 rad
Angle ∠ C = γ = 92.86659839826° = 92°51'58″ = 1.62108171836 rad

Height: ha = 11.98549906133
Height: hb = 9.98774921777
Height: hc = 7.49106191333

Median: ma = 13.22987565553
Median: mb = 11.91663752878
Median: mc = 7.61657731059

Inradius: r = 3.15439448982
Circumradius: R = 8.01100187891

Vertex coordinates: A[16; 0] B[0; 0] C[6.625; 7.49106191333]
Centroid: CG[7.54216666667; 2.49768730444]
Coordinates of the circumscribed circle: U[8; -0.40105009395]
Coordinates of the inscribed circle: I[7; 3.15439448982]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.3755167127° = 141°22'31″ = 0.67441305067 rad
∠ B' = β' = 131.4910816856° = 131°29'27″ = 0.84766449633 rad
∠ C' = γ' = 87.13440160174° = 87°8'2″ = 1.62108171836 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 = 10 ; ; b = 12 ; ; c = 16 ; ;

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

p = a+b+c = 10+12+16 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-10)(19-12)(19-16) } ; ; T = sqrt{ 3591 } = 59.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.92 }{ 10 } = 11.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.92 }{ 12 } = 9.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.92 }{ 16 } = 7.49 ; ;

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{ 12**2+16**2-10**2 }{ 2 * 12 * 16 } ) = 38° 37'29" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+16**2-12**2 }{ 2 * 10 * 16 } ) = 48° 30'33" ; ; gamma = 180° - alpha - beta = 180° - 38° 37'29" - 48° 30'33" = 92° 51'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.92 }{ 19 } = 3.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 38° 37'29" } = 8.01 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 16**2 - 10**2 } }{ 2 } = 13.229 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 10**2 - 12**2 } }{ 2 } = 11.916 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 10**2 - 16**2 } }{ 2 } = 7.616 ; ;
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