170 366 427 triangle

Obtuse scalene triangle.

Sides: a = 170   b = 366   c = 427

Area: T = 30726.73549703
Perimeter: p = 963
Semiperimeter: s = 481.5

Angle ∠ A = α = 23.15551106019° = 23°9'18″ = 0.40441329187 rad
Angle ∠ B = β = 57.84219547775° = 57°50'31″ = 1.01095325567 rad
Angle ∠ C = γ = 99.00329346206° = 99°11″ = 1.72879271783 rad

Height: ha = 361.4910999651
Height: hb = 167.9065655576
Height: hc = 143.9199133351

Median: ma = 388.4811016267
Median: mb = 268.5621910926
Median: mc = 189.3329738816

Inradius: r = 63.81546105303
Circumradius: R = 216.163305821

Vertex coordinates: A[427; 0] B[0; 0] C[90.48436065574; 143.9199133351]
Centroid: CG[172.4954535519; 47.97330444502]
Coordinates of the circumscribed circle: U[213.5; -33.82662876288]
Coordinates of the inscribed circle: I[115.5; 63.81546105303]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.8454889398° = 156°50'42″ = 0.40441329187 rad
∠ B' = β' = 122.1588045222° = 122°9'29″ = 1.01095325567 rad
∠ C' = γ' = 80.99770653794° = 80°59'49″ = 1.72879271783 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 = 170 ; ; b = 366 ; ; c = 427 ; ;

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

p = a+b+c = 170+366+427 = 963 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 963 }{ 2 } = 481.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 481.5 * (481.5-170)(481.5-366)(481.5-427) } ; ; T = sqrt{ 944132241.94 } = 30726.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30726.73 }{ 170 } = 361.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30726.73 }{ 366 } = 167.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30726.73 }{ 427 } = 143.92 ; ;

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{ 170**2-366**2-427**2 }{ 2 * 366 * 427 } ) = 23° 9'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 366**2-170**2-427**2 }{ 2 * 170 * 427 } ) = 57° 50'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 427**2-170**2-366**2 }{ 2 * 366 * 170 } ) = 99° 11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30726.73 }{ 481.5 } = 63.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 170 }{ 2 * sin 23° 9'18" } = 216.16 ; ;




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

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