Triangle calculator ASA

Please enter the side of the triangle and two adjacent angles
°
°


Acute isosceles triangle.

Sides: a = 287.9398524157   b = 287.9398524157   c = 100

Area: T = 14178.2054549
Perimeter: p = 675.8777048314
Semiperimeter: s = 337.9398524157

Angle ∠ A = α = 80° = 1.39662634016 rad
Angle ∠ B = β = 80° = 1.39662634016 rad
Angle ∠ C = γ = 20° = 0.34990658504 rad

Height: ha = 98.48107753012
Height: hb = 98.48107753012
Height: hc = 283.5644090981

Median: ma = 160.3976846676
Median: mb = 160.3976846676
Median: mc = 283.5644090981

Inradius: r = 41.95549815589
Circumradius: R = 146.1990220008

Vertex coordinates: A[100; 0] B[0; 0] C[50; 283.5644090981]
Centroid: CG[50; 94.52113636603]
Coordinates of the circumscribed circle: U[50; 137.3743870973]
Coordinates of the inscribed circle: I[50; 41.95549815589]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 100° = 1.39662634016 rad
∠ B' = β' = 100° = 1.39662634016 rad
∠ C' = γ' = 160° = 0.34990658504 rad

Calculate another triangle




How did we calculate this triangle?

1. Calculate the third unknown inner angle

 alpha = 80° ; ; beta = 80° ; ; ; ; alpha + beta + gamma = 180° ; ; ; ; gamma = 180° - alpha - beta = 180° - 80° - 80° = 20° ; ;

2. By using the law of sines, we calculate unknown side a

c = 100 ; ; ; ; fraction{ a }{ c } = fraction{ sin alpha }{ sin gamma } ; ; ; ; a = c * fraction{ sin alpha }{ sin gamma } ; ; ; ; a = 100 * fraction{ sin 80° }{ sin 20° } = 287.94 ; ;

3. By using the law of sines, we calculate last unknown side b

 fraction{ b }{ c } = fraction{ sin beta }{ sin gamma } ; ; ; ; b = c * fraction{ sin beta }{ sin gamma } ; ; ; ; b = 100 * fraction{ sin 80° }{ sin 20° } = 287.94 ; ;
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 = 287.94 ; ; b = 287.94 ; ; c = 100 ; ;

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

p = a+b+c = 287.94+287.94+100 = 675.88 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 675.88 }{ 2 } = 337.94 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 337.94 * (337.94-287.94)(337.94-287.94)(337.94-100) } ; ; T = sqrt{ 201021484.23 } = 14178.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14178.2 }{ 287.94 } = 98.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14178.2 }{ 287.94 } = 98.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14178.2 }{ 100 } = 283.56 ; ;

8. 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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 287.94**2+100**2-287.94**2 }{ 2 * 287.94 * 100 } ) = 80° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 287.94**2+100**2-287.94**2 }{ 2 * 287.94 * 100 } ) = 80° ; ; gamma = 180° - alpha - beta = 180° - 80° - 80° = 20° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14178.2 }{ 337.94 } = 41.95 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 287.94 }{ 2 * sin 80° } = 146.19 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 287.94**2+2 * 100**2 - 287.94**2 } }{ 2 } = 160.397 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 287.94**2 - 287.94**2 } }{ 2 } = 160.397 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 287.94**2+2 * 287.94**2 - 100**2 } }{ 2 } = 283.564 ; ;
Calculate another triangle

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

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