7 16 20 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 16   c = 20

Area: T = 50.71442731388
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 18.47994319838° = 18°28'46″ = 0.3232526932 rad
Angle ∠ B = β = 46.42664064704° = 46°25'35″ = 0.81102936528 rad
Angle ∠ C = γ = 115.0944161546° = 115°5'39″ = 2.00987720688 rad

Height: ha = 14.49897923254
Height: hb = 6.33992841424
Height: hc = 5.07114273139

Median: ma = 17.76993556439
Median: mb = 12.66988594593
Median: mc = 7.24656883731

Inradius: r = 2.35988034018
Circumradius: R = 11.04222562592

Vertex coordinates: A[20; 0] B[0; 0] C[4.825; 5.07114273139]
Centroid: CG[8.275; 1.69904757713]
Coordinates of the circumscribed circle: U[10; -4.68330997528]
Coordinates of the inscribed circle: I[5.5; 2.35988034018]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.5210568016° = 161°31'14″ = 0.3232526932 rad
∠ B' = β' = 133.574359353° = 133°34'25″ = 0.81102936528 rad
∠ C' = γ' = 64.90658384542° = 64°54'21″ = 2.00987720688 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 = 16 ; ; c = 20 ; ;

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

p = a+b+c = 7+16+20 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-7)(21.5-16)(21.5-20) } ; ; T = sqrt{ 2571.94 } = 50.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 50.71 }{ 7 } = 14.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 50.71 }{ 16 } = 6.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 50.71 }{ 20 } = 5.07 ; ;

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**2-16**2-20**2 }{ 2 * 16 * 20 } ) = 18° 28'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-7**2-20**2 }{ 2 * 7 * 20 } ) = 46° 25'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-7**2-16**2 }{ 2 * 16 * 7 } ) = 115° 5'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 50.71 }{ 21.5 } = 2.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 18° 28'46" } = 11.04 ; ;




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

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