4 15 16 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 15   c = 16

Area: T = 29.76547022495
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 14.36215115629° = 14°21'41″ = 0.25106556623 rad
Angle ∠ B = β = 68.45877326556° = 68°27'28″ = 1.19548128333 rad
Angle ∠ C = γ = 97.18107557815° = 97°10'51″ = 1.6966124158 rad

Height: ha = 14.88223511247
Height: hb = 3.96986269666
Height: hc = 3.72105877812

Median: ma = 15.37985564992
Median: mb = 8.93302855497
Median: mc = 7.51766481892

Inradius: r = 1.70108401285
Circumradius: R = 8.06332420909

Vertex coordinates: A[16; 0] B[0; 0] C[1.469875; 3.72105877812]
Centroid: CG[5.82329166667; 1.24401959271]
Coordinates of the circumscribed circle: U[8; -1.00879052614]
Coordinates of the inscribed circle: I[2.5; 1.70108401285]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.6388488437° = 165°38'19″ = 0.25106556623 rad
∠ B' = β' = 111.5422267344° = 111°32'32″ = 1.19548128333 rad
∠ C' = γ' = 82.81992442185° = 82°49'9″ = 1.6966124158 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 = 4 ; ; b = 15 ; ; c = 16 ; ;

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

p = a+b+c = 4+15+16 = 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 * (17.5-4)(17.5-15)(17.5-16) } ; ; T = sqrt{ 885.94 } = 29.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.76 }{ 4 } = 14.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.76 }{ 15 } = 3.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.76 }{ 16 } = 3.72 ; ;

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{ 4**2-15**2-16**2 }{ 2 * 15 * 16 } ) = 14° 21'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-4**2-16**2 }{ 2 * 4 * 16 } ) = 68° 27'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-4**2-15**2 }{ 2 * 15 * 4 } ) = 97° 10'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.76 }{ 17.5 } = 1.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 14° 21'41" } = 8.06 ; ;




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

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