5 7 10 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 7   c = 10

Area: T = 16.24880768093
Perimeter: p = 22
Semiperimeter: s = 11

Angle ∠ A = α = 27.66604498993° = 27°39'38″ = 0.48327659233 rad
Angle ∠ B = β = 40.53658021113° = 40°32'9″ = 0.70774832118 rad
Angle ∠ C = γ = 111.8043747989° = 111°48'13″ = 1.95113435185 rad

Height: ha = 6.49992307237
Height: hb = 4.64223076598
Height: hc = 3.25496153619

Median: ma = 8.26113558209
Median: mb = 7.08987234394
Median: mc = 3.46441016151

Inradius: r = 1.47770978918
Circumradius: R = 5.38552527303

Vertex coordinates: A[10; 0] B[0; 0] C[3.8; 3.25496153619]
Centroid: CG[4.6; 1.08332051206]
Coordinates of the circumscribed circle: U[5; -22.0002367284]
Coordinates of the inscribed circle: I[4; 1.47770978918]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.3439550101° = 152°20'22″ = 0.48327659233 rad
∠ B' = β' = 139.4644197889° = 139°27'51″ = 0.70774832118 rad
∠ C' = γ' = 68.19662520106° = 68°11'47″ = 1.95113435185 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 = 5 ; ; b = 7 ; ; c = 10 ; ;

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

p = a+b+c = 5+7+10 = 22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22 }{ 2 } = 11 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11 * (11-5)(11-7)(11-10) } ; ; T = sqrt{ 264 } = 16.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16.25 }{ 5 } = 6.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16.25 }{ 7 } = 4.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16.25 }{ 10 } = 3.25 ; ;

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{ 5**2-7**2-10**2 }{ 2 * 7 * 10 } ) = 27° 39'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-5**2-10**2 }{ 2 * 5 * 10 } ) = 40° 32'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10**2-5**2-7**2 }{ 2 * 7 * 5 } ) = 111° 48'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16.25 }{ 11 } = 1.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 27° 39'38" } = 5.39 ; ;




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

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