15 16 29 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 16   c = 29

Area: T = 79.37325393319
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 20.00662724699° = 20°23″ = 0.34991753257 rad
Angle ∠ B = β = 21.40333496394° = 21°24'12″ = 0.37435589222 rad
Angle ∠ C = γ = 138.5990377891° = 138°35'25″ = 2.41988584058 rad

Height: ha = 10.58330052443
Height: hb = 9.92215674165
Height: hc = 5.47439682298

Median: ma = 22.18767077323
Median: mb = 21.65664078277
Median: mc = 5.5

Inradius: r = 2.64657513111
Circumradius: R = 21.92219394345

Vertex coordinates: A[29; 0] B[0; 0] C[13.96655172414; 5.47439682298]
Centroid: CG[14.32218390805; 1.82546560766]
Coordinates of the circumscribed circle: U[14.5; -16.44114545759]
Coordinates of the inscribed circle: I[14; 2.64657513111]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.994372753° = 159°59'37″ = 0.34991753257 rad
∠ B' = β' = 158.5976650361° = 158°35'48″ = 0.37435589222 rad
∠ C' = γ' = 41.41096221093° = 41°24'35″ = 2.41988584058 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 = 15 ; ; b = 16 ; ; c = 29 ; ;

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

p = a+b+c = 15+16+29 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-15)(30-16)(30-29) } ; ; T = sqrt{ 6300 } = 79.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.37 }{ 15 } = 10.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.37 }{ 16 } = 9.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.37 }{ 29 } = 5.47 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 16**2+29**2-15**2 }{ 2 * 16 * 29 } ) = 20° 23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 15**2+29**2-16**2 }{ 2 * 15 * 29 } ) = 21° 24'12" ; ; gamma = 180° - alpha - beta = 180° - 20° 23" - 21° 24'12" = 138° 35'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.37 }{ 30 } = 2.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 15 }{ 2 * sin 20° 23" } = 21.92 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 29**2 - 15**2 } }{ 2 } = 22.187 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 15**2 - 16**2 } }{ 2 } = 21.656 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 15**2 - 29**2 } }{ 2 } = 5.5 ; ;
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