16 17 30 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 17   c = 30

Area: T = 103.051065502
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 23.83660070776° = 23°50'10″ = 0.4166016804 rad
Angle ∠ B = β = 25.42880757607° = 25°25'41″ = 0.44438036445 rad
Angle ∠ C = γ = 130.7365917162° = 130°44'9″ = 2.28217722051 rad

Height: ha = 12.88113318775
Height: hb = 12.12436064729
Height: hc = 6.8770043668

Median: ma = 23.03325856126
Median: mb = 22.4898886144
Median: mc = 6.8922024376

Inradius: r = 3.27114493657
Circumradius: R = 19.79660895989

Vertex coordinates: A[30; 0] B[0; 0] C[14.45; 6.8770043668]
Centroid: CG[14.81766666667; 2.2990014556]
Coordinates of the circumscribed circle: U[15; -12.91884040581]
Coordinates of the inscribed circle: I[14.5; 3.27114493657]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.1643992922° = 156°9'50″ = 0.4166016804 rad
∠ B' = β' = 154.5721924239° = 154°34'19″ = 0.44438036445 rad
∠ C' = γ' = 49.26440828384° = 49°15'51″ = 2.28217722051 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 = 16 ; ; b = 17 ; ; c = 30 ; ;

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

p = a+b+c = 16+17+30 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-16)(31.5-17)(31.5-30) } ; ; T = sqrt{ 10619.44 } = 103.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 103.05 }{ 16 } = 12.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 103.05 }{ 17 } = 12.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 103.05 }{ 30 } = 6.87 ; ;

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**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 23° 50'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-16**2-30**2 }{ 2 * 16 * 30 } ) = 25° 25'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-16**2-17**2 }{ 2 * 17 * 16 } ) = 130° 44'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 103.05 }{ 31.5 } = 3.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 23° 50'10" } = 19.8 ; ;




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