3 7 9 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 7   c = 9

Area: T = 8.78656416954
Perimeter: p = 19
Semiperimeter: s = 9.5

Angle ∠ A = α = 16.1955116739° = 16°11'42″ = 0.28326581098 rad
Angle ∠ B = β = 40.60110607311° = 40°36'4″ = 0.70986221896 rad
Angle ∠ C = γ = 123.204382253° = 123°12'14″ = 2.15503123542 rad

Height: ha = 5.85770944636
Height: hb = 2.51101833415
Height: hc = 1.95223648212

Median: ma = 7.92114897589
Median: mb = 5.72327615711
Median: mc = 2.95880398915

Inradius: r = 0.9254804389
Circumradius: R = 5.3788093216

Vertex coordinates: A[9; 0] B[0; 0] C[2.27877777778; 1.95223648212]
Centroid: CG[3.75992592593; 0.65107882737]
Coordinates of the circumscribed circle: U[4.5; -2.94551462849]
Coordinates of the inscribed circle: I[2.5; 0.9254804389]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.8054883261° = 163°48'18″ = 0.28326581098 rad
∠ B' = β' = 139.3998939269° = 139°23'56″ = 0.70986221896 rad
∠ C' = γ' = 56.796617747° = 56°47'46″ = 2.15503123542 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 = 3 ; ; b = 7 ; ; c = 9 ; ;

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

p = a+b+c = 3+7+9 = 19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19 }{ 2 } = 9.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.5 * (9.5-3)(9.5-7)(9.5-9) } ; ; T = sqrt{ 77.19 } = 8.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.79 }{ 3 } = 5.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.79 }{ 7 } = 2.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.79 }{ 9 } = 1.95 ; ;

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{ 3**2-7**2-9**2 }{ 2 * 7 * 9 } ) = 16° 11'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-3**2-9**2 }{ 2 * 3 * 9 } ) = 40° 36'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9**2-3**2-7**2 }{ 2 * 7 * 3 } ) = 123° 12'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.79 }{ 9.5 } = 0.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 16° 11'42" } = 5.38 ; ;




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

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