8 14 16 triangle

Acute scalene triangle.

Sides: a = 8   b = 14   c = 16

Area: T = 55.99110707167
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 29.99547255274° = 29°59'41″ = 0.52435067187 rad
Angle ∠ B = β = 61.02884677763° = 61°1'42″ = 1.06551477001 rad
Angle ∠ C = γ = 88.97768066963° = 88°58'37″ = 1.55329382348 rad

Height: ha = 13.99877676792
Height: hb = 7.99987243881
Height: hc = 6.99988838396

Median: ma = 14.49113767462
Median: mb = 10.53656537529
Median: mc = 8.12440384046

Inradius: r = 2.94768984588
Circumradius: R = 8.00112758153

Vertex coordinates: A[16; 0] B[0; 0] C[3.875; 6.99988838396]
Centroid: CG[6.625; 2.33329612799]
Coordinates of the circumscribed circle: U[8; 0.14328799253]
Coordinates of the inscribed circle: I[5; 2.94768984588]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0055274473° = 150°19″ = 0.52435067187 rad
∠ B' = β' = 118.9721532224° = 118°58'18″ = 1.06551477001 rad
∠ C' = γ' = 91.02331933037° = 91°1'23″ = 1.55329382348 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 = 8 ; ; b = 14 ; ; c = 16 ; ;

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

p = a+b+c = 8+14+16 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-8)(19-14)(19-16) } ; ; T = sqrt{ 3135 } = 55.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.99 }{ 8 } = 14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.99 }{ 14 } = 8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.99 }{ 16 } = 7 ; ;

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{ 8**2-14**2-16**2 }{ 2 * 14 * 16 } ) = 29° 59'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-8**2-16**2 }{ 2 * 8 * 16 } ) = 61° 1'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-8**2-14**2 }{ 2 * 14 * 8 } ) = 88° 58'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.99 }{ 19 } = 2.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 29° 59'41" } = 8 ; ;




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

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