3 15 16 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 15   c = 16

Area: T = 21.81774242293
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 10.47553138432° = 10°28'31″ = 0.18328287167 rad
Angle ∠ B = β = 65.37656816478° = 65°22'32″ = 1.14110208955 rad
Angle ∠ C = γ = 104.1499004509° = 104°8'56″ = 1.81877430414 rad

Height: ha = 14.54549494862
Height: hb = 2.90989898972
Height: hc = 2.72771780287

Median: ma = 15.43553490404
Median: mb = 8.73221245983
Median: mc = 7.28801098893

Inradius: r = 1.28333778958
Circumradius: R = 8.25502864733

Vertex coordinates: A[16; 0] B[0; 0] C[1.25; 2.72771780287]
Centroid: CG[5.75; 0.90990593429]
Coordinates of the circumscribed circle: U[8; -2.01767366935]
Coordinates of the inscribed circle: I[2; 1.28333778958]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.5254686157° = 169°31'29″ = 0.18328287167 rad
∠ B' = β' = 114.6244318352° = 114°37'28″ = 1.14110208955 rad
∠ C' = γ' = 75.85109954911° = 75°51'4″ = 1.81877430414 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 = 3 ; ; b = 15 ; ; c = 16 ; ;

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

p = a+b+c = 3+15+16 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-3)(17-15)(17-16) } ; ; T = sqrt{ 476 } = 21.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.82 }{ 3 } = 14.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.82 }{ 15 } = 2.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.82 }{ 16 } = 2.73 ; ;

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{ 3**2-15**2-16**2 }{ 2 * 15 * 16 } ) = 10° 28'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-3**2-16**2 }{ 2 * 3 * 16 } ) = 65° 22'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-3**2-15**2 }{ 2 * 15 * 3 } ) = 104° 8'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.82 }{ 17 } = 1.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 10° 28'31" } = 8.25 ; ;




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