7 27 30 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 27   c = 30

Area: T = 89.44327191
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 12.75987404169° = 12°45'31″ = 0.22326820287 rad
Angle ∠ B = β = 58.41218644948° = 58°24'43″ = 1.01994793577 rad
Angle ∠ C = γ = 108.8299395088° = 108°49'46″ = 1.89994312672 rad

Height: ha = 25.55550626
Height: hb = 6.62553866
Height: hc = 5.963284794

Median: ma = 28.32440180765
Median: mb = 17.09553209973
Median: mc = 12.80662484749

Inradius: r = 2.79550849719
Circumradius: R = 15.84881317905

Vertex coordinates: A[30; 0] B[0; 0] C[3.66766666667; 5.963284794]
Centroid: CG[11.22222222222; 1.988761598]
Coordinates of the circumscribed circle: U[15; -5.11550054985]
Coordinates of the inscribed circle: I[5; 2.79550849719]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.2411259583° = 167°14'29″ = 0.22326820287 rad
∠ B' = β' = 121.5888135505° = 121°35'17″ = 1.01994793577 rad
∠ C' = γ' = 71.17106049117° = 71°10'14″ = 1.89994312672 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 = 7 ; ; b = 27 ; ; c = 30 ; ;

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

p = a+b+c = 7+27+30 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-7)(32-27)(32-30) } ; ; T = sqrt{ 8000 } = 89.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 89.44 }{ 7 } = 25.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 89.44 }{ 27 } = 6.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 89.44 }{ 30 } = 5.96 ; ;

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{ 7**2-27**2-30**2 }{ 2 * 27 * 30 } ) = 12° 45'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-7**2-30**2 }{ 2 * 7 * 30 } ) = 58° 24'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-7**2-27**2 }{ 2 * 27 * 7 } ) = 108° 49'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 89.44 }{ 32 } = 2.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 12° 45'31" } = 15.85 ; ;




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

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