8 16 17 triangle

Acute scalene triangle.

Sides: a = 8   b = 16   c = 17

Area: T = 63.52990287979
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 27.84878490371° = 27°50'52″ = 0.48660366553 rad
Angle ∠ B = β = 69.10773811539° = 69°6'27″ = 1.20661513386 rad
Angle ∠ C = γ = 83.0454769809° = 83°2'41″ = 1.44994046597 rad

Height: ha = 15.88222571995
Height: hb = 7.94111285997
Height: hc = 7.4744003388

Median: ma = 16.0165617378
Median: mb = 10.60766017178
Median: mc = 9.36774969976

Inradius: r = 3.09989770145
Circumradius: R = 8.56330145824

Vertex coordinates: A[17; 0] B[0; 0] C[2.85329411765; 7.4744003388]
Centroid: CG[6.61876470588; 2.49113344627]
Coordinates of the circumscribed circle: U[8.5; 1.03769275471]
Coordinates of the inscribed circle: I[4.5; 3.09989770145]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.1522150963° = 152°9'8″ = 0.48660366553 rad
∠ B' = β' = 110.8932618846° = 110°53'33″ = 1.20661513386 rad
∠ C' = γ' = 96.9555230191° = 96°57'19″ = 1.44994046597 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 = 16 ; ; c = 17 ; ;

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

p = a+b+c = 8+16+17 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-8)(20.5-16)(20.5-17) } ; ; T = sqrt{ 4035.94 } = 63.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 63.53 }{ 8 } = 15.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 63.53 }{ 16 } = 7.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 63.53 }{ 17 } = 7.47 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 8**2-16**2-17**2 }{ 2 * 16 * 17 } ) = 27° 50'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-8**2-17**2 }{ 2 * 8 * 17 } ) = 69° 6'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-8**2-16**2 }{ 2 * 16 * 8 } ) = 83° 2'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 63.53 }{ 20.5 } = 3.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 27° 50'52" } = 8.56 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.