7 13 15 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 13   c = 15

Area: T = 45.46663336987
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 27.7965772496° = 27°47'45″ = 0.48551277482 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 92.2044227504° = 92°12'15″ = 1.60992673542 rad

Height: ha = 12.99903810568
Height: hb = 6.9954820569
Height: hc = 6.06221778265

Median: ma = 13.59222772191
Median: mb = 9.7343961167
Median: mc = 7.26329195232

Inradius: r = 2.59880762114
Circumradius: R = 7.50655534995

Vertex coordinates: A[15; 0] B[0; 0] C[3.5; 6.06221778265]
Centroid: CG[6.16766666667; 2.02107259422]
Coordinates of the circumscribed circle: U[7.5; -0.28986751346]
Coordinates of the inscribed circle: I[4.5; 2.59880762114]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.2044227504° = 152°12'15″ = 0.48551277482 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 87.7965772496° = 87°47'45″ = 1.60992673542 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 = 13 ; ; c = 15 ; ;

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

p = a+b+c = 7+13+15 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-7)(17.5-13)(17.5-15) } ; ; T = sqrt{ 2067.19 } = 45.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 45.47 }{ 7 } = 12.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 45.47 }{ 13 } = 6.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 45.47 }{ 15 } = 6.06 ; ;

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**2-13**2-15**2 }{ 2 * 13 * 15 } ) = 27° 47'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-7**2-15**2 }{ 2 * 7 * 15 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-7**2-13**2 }{ 2 * 13 * 7 } ) = 92° 12'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 45.47 }{ 17.5 } = 2.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 27° 47'45" } = 7.51 ; ;




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

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