14 16 29 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 16   c = 29

Area: T = 55.55657152775
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 13.85549244913° = 13°51'18″ = 0.242181405 rad
Angle ∠ B = β = 15.88329774841° = 15°52'59″ = 0.27772102521 rad
Angle ∠ C = γ = 150.2622098025° = 150°15'44″ = 2.62325683515 rad

Height: ha = 7.93765307539
Height: hb = 6.94444644097
Height: hc = 3.83114286398

Median: ma = 22.34994966386
Median: mb = 21.31990056053
Median: mc = 3.96986269666

Inradius: r = 1.88332445857
Circumradius: R = 29.23219159584

Vertex coordinates: A[29; 0] B[0; 0] C[13.46655172414; 3.83114286398]
Centroid: CG[14.15551724138; 1.27771428799]
Coordinates of the circumscribed circle: U[14.5; -25.38221770263]
Coordinates of the inscribed circle: I[13.5; 1.88332445857]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.1455075509° = 166°8'42″ = 0.242181405 rad
∠ B' = β' = 164.1177022516° = 164°7'1″ = 0.27772102521 rad
∠ C' = γ' = 29.73879019754° = 29°44'16″ = 2.62325683515 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 = 14 ; ; b = 16 ; ; c = 29 ; ;

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

p = a+b+c = 14+16+29 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-14)(29.5-16)(29.5-29) } ; ; T = sqrt{ 3086.44 } = 55.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.56 }{ 14 } = 7.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.56 }{ 16 } = 6.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.56 }{ 29 } = 3.83 ; ;

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{ 14**2-16**2-29**2 }{ 2 * 16 * 29 } ) = 13° 51'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-14**2-29**2 }{ 2 * 14 * 29 } ) = 15° 52'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-14**2-16**2 }{ 2 * 16 * 14 } ) = 150° 15'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.56 }{ 29.5 } = 1.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 13° 51'18" } = 29.23 ; ;




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

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