Triangle calculator SAS

Please enter two sides of the triangle and the included angle
°


Right scalene triangle.

Sides: a = 288   b = 32   c = 289.772232442

Area: T = 4608
Perimeter: p = 609.772232442
Semiperimeter: s = 304.886616221

Angle ∠ A = α = 83.66598082541° = 83°39'35″ = 1.46601391056 rad
Angle ∠ B = β = 6.34401917459° = 6°20'25″ = 0.11106572212 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 32
Height: hb = 288
Height: hc = 31.80442795096

Median: ma = 147.5132711317
Median: mb = 288.4444102037
Median: mc = 144.886616221

Inradius: r = 15.11438377898
Circumradius: R = 144.886616221

Vertex coordinates: A[289.772232442; 0] B[0; 0] C[286.2398515586; 31.80442795096]
Centroid: CG[192.0043613336; 10.60114265032]
Coordinates of the circumscribed circle: U[144.886616221; 0]
Coordinates of the inscribed circle: I[272.886616221; 15.11438377898]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 96.34401917459° = 96°20'25″ = 1.46601391056 rad
∠ B' = β' = 173.6659808254° = 173°39'35″ = 0.11106572212 rad
∠ C' = γ' = 90° = 1.57107963268 rad

Calculate another triangle




How did we calculate this triangle?

1. Calculation of the third side c of the triangle using a Law of Cosines

a = 288 ; ; b = 32 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 288**2+32**2 - 2 * 288 * 32 * cos(90° ) } ; ; c = 289.77 ; ;


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 = 288 ; ; b = 32 ; ; c = 289.77 ; ;

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

p = a+b+c = 288+32+289.77 = 609.77 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 609.77 }{ 2 } = 304.89 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 304.89 * (304.89-288)(304.89-32)(304.89-289.77) } ; ; T = sqrt{ 21233664 } = 4608 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4608 }{ 288 } = 32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4608 }{ 32 } = 288 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4608 }{ 289.77 } = 31.8 ; ;

6. 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{ 288**2-32**2-289.77**2 }{ 2 * 32 * 289.77 } ) = 83° 39'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 32**2-288**2-289.77**2 }{ 2 * 288 * 289.77 } ) = 6° 20'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 289.77**2-288**2-32**2 }{ 2 * 32 * 288 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4608 }{ 304.89 } = 15.11 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 288 }{ 2 * sin 83° 39'35" } = 144.89 ; ;




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

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