13 16 25 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 16   c = 25

Area: T = 91.19221049214
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 27.12767531173° = 27°7'36″ = 0.47334511573 rad
Angle ∠ B = β = 34.13875931378° = 34°8'15″ = 0.5965813399 rad
Angle ∠ C = γ = 118.7365653745° = 118°44'8″ = 2.07223280974 rad

Height: ha = 14.03295546033
Height: hb = 11.39990131152
Height: hc = 7.29553683937

Median: ma = 19.95662020435
Median: mb = 18.24882875909
Median: mc = 7.5

Inradius: r = 3.37774853675
Circumradius: R = 14.25656200575

Vertex coordinates: A[25; 0] B[0; 0] C[10.76; 7.29553683937]
Centroid: CG[11.92; 2.43217894646]
Coordinates of the circumscribed circle: U[12.5; -6.85436634892]
Coordinates of the inscribed circle: I[11; 3.37774853675]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.8733246883° = 152°52'24″ = 0.47334511573 rad
∠ B' = β' = 145.8622406862° = 145°51'45″ = 0.5965813399 rad
∠ C' = γ' = 61.26443462551° = 61°15'52″ = 2.07223280974 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 = 13 ; ; b = 16 ; ; c = 25 ; ;

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

p = a+b+c = 13+16+25 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-13)(27-16)(27-25) } ; ; T = sqrt{ 8316 } = 91.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 91.19 }{ 13 } = 14.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 91.19 }{ 16 } = 11.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 91.19 }{ 25 } = 7.3 ; ;

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{ 13**2-16**2-25**2 }{ 2 * 16 * 25 } ) = 27° 7'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-13**2-25**2 }{ 2 * 13 * 25 } ) = 34° 8'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-13**2-16**2 }{ 2 * 16 * 13 } ) = 118° 44'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 91.19 }{ 27 } = 3.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 27° 7'36" } = 14.26 ; ;




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

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