8 17 18 triangle

Acute scalene triangle.

Sides: a = 8   b = 17   c = 18

Area: T = 67.61224064059
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 26.22658839295° = 26°13'33″ = 0.45877280238 rad
Angle ∠ B = β = 69.89444902121° = 69°53'40″ = 1.22198889832 rad
Angle ∠ C = γ = 83.88796258585° = 83°52'47″ = 1.46439756466 rad

Height: ha = 16.90331016015
Height: hb = 7.95444007536
Height: hc = 7.51224896007

Median: ma = 17.04440605491
Median: mb = 11.03440382454
Median: mc = 9.77224101428

Inradius: r = 3.14547630886
Circumradius: R = 9.05215932287

Vertex coordinates: A[18; 0] B[0; 0] C[2.75; 7.51224896007]
Centroid: CG[6.91766666667; 2.50441632002]
Coordinates of the circumscribed circle: U[9; 0.96550595722]
Coordinates of the inscribed circle: I[4.5; 3.14547630886]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.7744116071° = 153°46'27″ = 0.45877280238 rad
∠ B' = β' = 110.1065509788° = 110°6'20″ = 1.22198889832 rad
∠ C' = γ' = 96.12203741415° = 96°7'13″ = 1.46439756466 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 = 17 ; ; c = 18 ; ;

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

p = a+b+c = 8+17+18 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-8)(21.5-17)(21.5-18) } ; ; T = sqrt{ 4571.44 } = 67.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 67.61 }{ 8 } = 16.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 67.61 }{ 17 } = 7.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 67.61 }{ 18 } = 7.51 ; ;

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**2-17**2-18**2 }{ 2 * 17 * 18 } ) = 26° 13'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-8**2-18**2 }{ 2 * 8 * 18 } ) = 69° 53'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-8**2-17**2 }{ 2 * 17 * 8 } ) = 83° 52'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 67.61 }{ 21.5 } = 3.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 26° 13'33" } = 9.05 ; ;




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

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