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: h_a = 11.98549906133
Height: h_b = 9.98774921777
Height: h_c = 7.49106191333

Median: m_a = 13.22987565553
Median: m_b = 11.91663752878
Median: m_c = 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

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.

$a = 10 ; ; b = 12 ; ; c = 16 ; ;$

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

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

6. Inradius

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

7. Circumradius

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

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