5 15 16 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 15   c = 16

Area: T = 37.47699879904
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 18.19548723388° = 18°11'42″ = 0.31875604293 rad
Angle ∠ B = β = 69.51326848853° = 69°30'46″ = 1.21332252231 rad
Angle ∠ C = γ = 92.2922442776° = 92°17'33″ = 1.61108070011 rad

Height: ha = 14.98879951962
Height: hb = 4.99659983987
Height: hc = 4.68437484988

Median: ma = 15.3055227865
Median: mb = 9.17987798753
Median: mc = 7.81102496759

Inradius: r = 2.08216659995
Circumradius: R = 8.00664076903

Vertex coordinates: A[16; 0] B[0; 0] C[1.75; 4.68437484988]
Centroid: CG[5.91766666667; 1.56112494996]
Coordinates of the circumscribed circle: U[8; -0.32202563076]
Coordinates of the inscribed circle: I[3; 2.08216659995]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.8055127661° = 161°48'18″ = 0.31875604293 rad
∠ B' = β' = 110.4877315115° = 110°29'14″ = 1.21332252231 rad
∠ C' = γ' = 87.7087557224° = 87°42'27″ = 1.61108070011 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 = 5 ; ; b = 15 ; ; c = 16 ; ;

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

p = a+b+c = 5+15+16 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-5)(18-15)(18-16) } ; ; T = sqrt{ 1404 } = 37.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 37.47 }{ 5 } = 14.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 37.47 }{ 15 } = 5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 37.47 }{ 16 } = 4.68 ; ;

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{ 5**2-15**2-16**2 }{ 2 * 15 * 16 } ) = 18° 11'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-5**2-16**2 }{ 2 * 5 * 16 } ) = 69° 30'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-5**2-15**2 }{ 2 * 15 * 5 } ) = 92° 17'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 37.47 }{ 18 } = 2.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 18° 11'42" } = 8.01 ; ;




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