4 28 30 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 28   c = 30

Area: T = 50.11098792655
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 6.8522238335° = 6°51'8″ = 0.12195941201 rad
Angle ∠ B = β = 56.63329870308° = 56°37'59″ = 0.98884320889 rad
Angle ∠ C = γ = 116.5154774634° = 116°30'53″ = 2.03435664446 rad

Height: ha = 25.05549396327
Height: hb = 3.57992770904
Height: hc = 3.34106586177

Median: ma = 28.94882296523
Median: mb = 16.18664140562
Median: mc = 13.22987565553

Inradius: r = 1.61664477182
Circumradius: R = 16.76331615225

Vertex coordinates: A[30; 0] B[0; 0] C[2.2; 3.34106586177]
Centroid: CG[10.73333333333; 1.11435528726]
Coordinates of the circumscribed circle: U[15; -7.48435542511]
Coordinates of the inscribed circle: I[3; 1.61664477182]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.1487761665° = 173°8'52″ = 0.12195941201 rad
∠ B' = β' = 123.3677012969° = 123°22'1″ = 0.98884320889 rad
∠ C' = γ' = 63.48552253657° = 63°29'7″ = 2.03435664446 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 = 4 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 4+28+30 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-4)(31-28)(31-30) } ; ; T = sqrt{ 2511 } = 50.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 50.11 }{ 4 } = 25.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 50.11 }{ 28 } = 3.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 50.11 }{ 30 } = 3.34 ; ;

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{ 4**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 6° 51'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-4**2-30**2 }{ 2 * 4 * 30 } ) = 56° 37'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-4**2-28**2 }{ 2 * 28 * 4 } ) = 116° 30'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 50.11 }{ 31 } = 1.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 6° 51'8" } = 16.76 ; ;




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

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