Triangle calculator ASA

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


Acute isosceles triangle.

Sides: a = 166.1644014112   b = 166.1644014112   c = 200

Area: T = 13270.44882162
Perimeter: p = 532.3288028225
Semiperimeter: s = 266.1644014112

Angle ∠ A = α = 53° = 0.92550245036 rad
Angle ∠ B = β = 53° = 0.92550245036 rad
Angle ∠ C = γ = 74° = 1.29215436465 rad

Height: ha = 159.7277102009
Height: hb = 159.7277102009
Height: hc = 132.7044482162

Median: ma = 164.0220181369
Median: mb = 164.0220181369
Median: mc = 132.7044482162

Inradius: r = 49.85881608053
Circumradius: R = 104.0329943586

Vertex coordinates: A[200; 0] B[0; 0] C[100; 132.7044482162]
Centroid: CG[100; 44.23548273873]
Coordinates of the circumscribed circle: U[100; 28.67545385759]
Coordinates of the inscribed circle: I[100; 49.85881608053]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127° = 0.92550245036 rad
∠ B' = β' = 127° = 0.92550245036 rad
∠ C' = γ' = 106° = 1.29215436465 rad

Calculate another triangle




How did we calculate this triangle?

1. Calculate the third unknown inner angle

 alpha = 53° ; ; beta = 53° ; ; ; ; alpha + beta + gamma = 180° ; ; ; ; gamma = 180° - alpha - beta = 180° - 53° - 53° = 74° ; ;

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

c = 200 ; ; ; ; fraction{ a }{ c } = fraction{ sin( alpha ) }{ sin ( gamma ) } ; ; ; ; a = c * fraction{ sin( alpha ) }{ sin ( gamma ) } ; ; ; ; a = 200 * fraction{ sin(53° ) }{ sin (74° ) } = 166.16 ; ;

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 = 200 * fraction{ sin(53° ) }{ sin (74° ) } = 166.16 ; ;


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 = 166.16 ; ; b = 166.16 ; ; c = 200 ; ;

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

p = a+b+c = 166.16+166.16+200 = 532.33 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 532.33 }{ 2 } = 266.16 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 266.16 * (266.16-166.16)(266.16-166.16)(266.16-200) } ; ; T = sqrt{ 176104795.86 } = 13270.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13270.45 }{ 166.16 } = 159.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13270.45 }{ 166.16 } = 159.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13270.45 }{ 200 } = 132.7 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 166.16**2-166.16**2-200**2 }{ 2 * 166.16 * 200 } ) = 53° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 166.16**2-166.16**2-200**2 }{ 2 * 166.16 * 200 } ) = 53° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 200**2-166.16**2-166.16**2 }{ 2 * 166.16 * 166.16 } ) = 74° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13270.45 }{ 266.16 } = 49.86 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 166.16 }{ 2 * sin 53° } = 104.03 ; ;




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

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