16 23 30 triangle

Obtuse scalene triangle.

Sides: a = 16 b = 23 c = 30

Area: T = 181.7440027237
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 31.78883306171° = 31°47'18″ = 0.5554811033 rad
Angle ∠ B = β = 49.22223700378° = 49°13'21″ = 0.85990924228 rad
Angle ∠ C = γ = 98.98992993452° = 98°59'21″ = 1.72876891978 rad

Height: h_a = 22.71875034046
Height: h_b = 15.80334806293
Height: h_c = 12.11660018158

Median: m_a = 25.50549014897
Median: m_b = 21.11327923307
Median: m_c = 12.94221791055

Inradius: r = 5.26878268764
Circumradius: R = 15.1876527932

Vertex coordinates: A[30; 0] B[0; 0] C[10.45; 12.11660018158]
Centroid: CG[13.48333333333; 4.03986672719]
Coordinates of the circumscribed circle: U[15; -2.37328949894]
Coordinates of the inscribed circle: I[11.5; 5.26878268764]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.2121669383° = 148°12'42″ = 0.5554811033 rad
∠ B' = β' = 130.7787629962° = 130°46'39″ = 0.85990924228 rad
∠ C' = γ' = 81.01107006548° = 81°39″ = 1.72876891978 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.

$a = 16 ; ; b = 23 ; ; c = 30 ; ;$

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

$p = a+b+c = 16+23+30 = 69 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-16)(34.5-23)(34.5-30) } ; ; T = sqrt{ 33029.44 } = 181.74 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 181.74 }{ 16 } = 22.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 181.74 }{ 23 } = 15.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 181.74 }{ 30 } = 12.12 ; ;$

5. Calculation of the inner angles of the triangle using a Law of Cosines

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 16**2-23**2-30**2 }{ 2 * 23 * 30 } ) = 31° 47'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-16**2-30**2 }{ 2 * 16 * 30 } ) = 49° 13'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-16**2-23**2 }{ 2 * 23 * 16 } ) = 98° 59'21" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 181.74 }{ 34.5 } = 5.27 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 31° 47'18" } = 15.19 ; ;$

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