Triangle calculator SAS

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


Obtuse isosceles triangle.

Sides: a = 42   b = 42   c = 66.64216805845

Area: T = 851.9476578787
Perimeter: p = 150.6421680584
Semiperimeter: s = 75.32108402922

Angle ∠ A = α = 37.5° = 37°30' = 0.65444984695 rad
Angle ∠ B = β = 37.5° = 37°30' = 0.65444984695 rad
Angle ∠ C = γ = 105° = 1.83325957146 rad

Height: ha = 40.56988847041
Height: hb = 40.56988847041
Height: hc = 25.56879800184

Median: ma = 51.59902781109
Median: mb = 51.59902781109
Median: mc = 25.56879800184

Inradius: r = 11.31109011461
Circumradius: R = 34.49662722658

Vertex coordinates: A[66.64216805845; 0] B[0; 0] C[33.32108402922; 25.56879800184]
Centroid: CG[33.32108402922; 8.52326600061]
Coordinates of the circumscribed circle: U[33.32108402922; -8.92882922474]
Coordinates of the inscribed circle: I[33.32108402922; 11.31109011461]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.5° = 142°30' = 0.65444984695 rad
∠ B' = β' = 142.5° = 142°30' = 0.65444984695 rad
∠ C' = γ' = 75° = 1.83325957146 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 = 42 ; ; b = 42 ; ; gamma = 105° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 42**2+42**2 - 2 * 42 * 42 * cos(105° ) } ; ; c = 66.64 ; ;


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 = 42 ; ; b = 42 ; ; c = 66.64 ; ;

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

p = a+b+c = 42+42+66.64 = 150.64 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 150.64 }{ 2 } = 75.32 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 75.32 * (75.32-42)(75.32-42)(75.32-66.64) } ; ; T = sqrt{ 725812.97 } = 851.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 851.95 }{ 42 } = 40.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 851.95 }{ 42 } = 40.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 851.95 }{ 66.64 } = 25.57 ; ;

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{ 42**2-42**2-66.64**2 }{ 2 * 42 * 66.64 } ) = 37° 30' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 42**2-42**2-66.64**2 }{ 2 * 42 * 66.64 } ) = 37° 30' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 66.64**2-42**2-42**2 }{ 2 * 42 * 42 } ) = 105° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 851.95 }{ 75.32 } = 11.31 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 42 }{ 2 * sin 37° 30' } = 34.5 ; ;




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

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