8 15 17 triangle

Right scalene triangle.

Sides: a = 8   b = 15   c = 17

Area: T = 60
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 28.07224869359° = 28°4'21″ = 0.49899573263 rad
Angle ∠ B = β = 61.92875130641° = 61°55'39″ = 1.08108390005 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 15
Height: hb = 8
Height: hc = 7.05988235294

Median: ma = 15.52441746963
Median: mb = 10.96658560997
Median: mc = 8.5

Inradius: r = 3
Circumradius: R = 8.5

Vertex coordinates: A[17; 0] B[0; 0] C[3.76547058824; 7.05988235294]
Centroid: CG[6.92215686275; 2.35329411765]
Coordinates of the circumscribed circle: U[8.5; 0]
Coordinates of the inscribed circle: I[5; 3]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.9287513064° = 151°55'39″ = 0.49899573263 rad
∠ B' = β' = 118.0722486936° = 118°4'21″ = 1.08108390005 rad
∠ C' = γ' = 90° = 1.57107963268 rad

Calculate another triangle




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 = 8 ; ; b = 15 ; ; c = 17 ; ;

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

p = a+b+c = 8+15+17 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-8)(20-15)(20-17) } ; ; T = sqrt{ 3600 } = 60 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 60 }{ 8 } = 15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 60 }{ 15 } = 8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 60 }{ 17 } = 7.06 ; ;

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{ 8**2-15**2-17**2 }{ 2 * 15 * 17 } ) = 28° 4'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-8**2-17**2 }{ 2 * 8 * 17 } ) = 61° 55'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-8**2-15**2 }{ 2 * 15 * 8 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 60 }{ 20 } = 3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 28° 4'21" } = 8.5 ; ;




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