9 10 16 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 10   c = 16

Area: T = 40.90876704299
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 30.75435198081° = 30°45'13″ = 0.53767501772 rad
Angle ∠ B = β = 34.62221618397° = 34°37'20″ = 0.60442707183 rad
Angle ∠ C = γ = 114.6244318352° = 114°37'28″ = 2.00105717581 rad

Height: ha = 9.09105934289
Height: hb = 8.1821534086
Height: hc = 5.11334588037

Median: ma = 12.56598566871
Median: mb = 11.97991485507
Median: mc = 5.14878150705

Inradius: r = 2.33875811674
Circumradius: R = 8.88003055715

Vertex coordinates: A[16; 0] B[0; 0] C[7.406625; 5.11334588037]
Centroid: CG[7.80220833333; 1.70444862679]
Coordinates of the circumscribed circle: U[8; -3.66767939881]
Coordinates of the inscribed circle: I[7.5; 2.33875811674]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.2466480192° = 149°14'47″ = 0.53767501772 rad
∠ B' = β' = 145.378783816° = 145°22'40″ = 0.60442707183 rad
∠ C' = γ' = 65.37656816478° = 65°22'32″ = 2.00105717581 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 = 9 ; ; b = 10 ; ; c = 16 ; ;

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

p = a+b+c = 9+10+16 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-9)(17.5-10)(17.5-16) } ; ; T = sqrt{ 1673.44 } = 40.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.91 }{ 9 } = 9.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.91 }{ 10 } = 8.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.91 }{ 16 } = 5.11 ; ;

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{ 9**2-10**2-16**2 }{ 2 * 10 * 16 } ) = 30° 45'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-9**2-16**2 }{ 2 * 9 * 16 } ) = 34° 37'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-9**2-10**2 }{ 2 * 10 * 9 } ) = 114° 37'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.91 }{ 17.5 } = 2.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 30° 45'13" } = 8.8 ; ;




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