14 15 27 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 15   c = 27

Area: T = 71.38662731903
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 20.64218214998° = 20°38'31″ = 0.36602677488 rad
Angle ∠ B = β = 22.19216065663° = 22°11'30″ = 0.38773166009 rad
Angle ∠ C = γ = 137.1676571934° = 137°10' = 2.39440083039 rad

Height: ha = 10.19880390272
Height: hb = 9.51881697587
Height: hc = 5.28878720882

Median: ma = 20.68881608656
Median: mb = 20.15656443707
Median: mc = 5.31550729064

Inradius: r = 2.55495097568
Circumradius: R = 19.85767586827

Vertex coordinates: A[27; 0] B[0; 0] C[12.9632962963; 5.28878720882]
Centroid: CG[13.32109876543; 1.76326240294]
Coordinates of the circumscribed circle: U[13.5; -14.5621623034]
Coordinates of the inscribed circle: I[13; 2.55495097568]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.35881785° = 159°21'29″ = 0.36602677488 rad
∠ B' = β' = 157.8088393434° = 157°48'30″ = 0.38773166009 rad
∠ C' = γ' = 42.83334280661° = 42°50' = 2.39440083039 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 = 14 ; ; b = 15 ; ; c = 27 ; ;

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

p = a+b+c = 14+15+27 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-14)(28-15)(28-27) } ; ; T = sqrt{ 5096 } = 71.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 71.39 }{ 14 } = 10.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 71.39 }{ 15 } = 9.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 71.39 }{ 27 } = 5.29 ; ;

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{ 14**2-15**2-27**2 }{ 2 * 15 * 27 } ) = 20° 38'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-14**2-27**2 }{ 2 * 14 * 27 } ) = 22° 11'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-14**2-15**2 }{ 2 * 15 * 14 } ) = 137° 10' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 71.39 }{ 28 } = 2.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 20° 38'31" } = 19.86 ; ;




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

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