6 15 16 triangle

Acute scalene triangle.

Sides: a = 6   b = 15   c = 16

Area: T = 44.98326355386
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 22.01553695404° = 22°55″ = 0.38442406845 rad
Angle ∠ B = β = 69.57663846362° = 69°34'35″ = 1.21443369935 rad
Angle ∠ C = γ = 88.40882458234° = 88°24'30″ = 1.54330149755 rad

Height: ha = 14.99442118462
Height: hb = 5.99876847385
Height: hc = 5.62328294423

Median: ma = 15.21551240547
Median: mb = 9.47436476607
Median: mc = 8.15547532152

Inradius: r = 2.43114938129
Circumradius: R = 8.0033088207

Vertex coordinates: A[16; 0] B[0; 0] C[2.094375; 5.62328294423]
Centroid: CG[6.031125; 1.87442764808]
Coordinates of the circumscribed circle: U[8; 0.22223080058]
Coordinates of the inscribed circle: I[3.5; 2.43114938129]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.985463046° = 157°59'5″ = 0.38442406845 rad
∠ B' = β' = 110.4243615364° = 110°25'25″ = 1.21443369935 rad
∠ C' = γ' = 91.59217541766° = 91°35'30″ = 1.54330149755 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 = 6 ; ; b = 15 ; ; c = 16 ; ;

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

p = a+b+c = 6+15+16 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-6)(18.5-15)(18.5-16) } ; ; T = sqrt{ 2023.44 } = 44.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.98 }{ 6 } = 14.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.98 }{ 15 } = 6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.98 }{ 16 } = 5.62 ; ;

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{ 6**2-15**2-16**2 }{ 2 * 15 * 16 } ) = 22° 55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-6**2-16**2 }{ 2 * 6 * 16 } ) = 69° 34'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-6**2-15**2 }{ 2 * 15 * 6 } ) = 88° 24'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.98 }{ 18.5 } = 2.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 22° 55" } = 8 ; ;




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