# Triangle calculator ASA

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

### Right isosceles triangle.

Sides: a = 63.64396103068   b = 45   c = 45

Area: T = 1012.5
Perimeter: p = 153.6439610307
Semiperimeter: s = 76.82198051534

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 31.82198051534
Height: hb = 45
Height: hc = 45

Median: ma = 31.82198051534
Median: mb = 50.31215294937
Median: mc = 50.31215294937

Inradius: r = 13.18801948466
Circumradius: R = 31.82198051534

Vertex coordinates: A[45; 0] B[0; 0] C[45; 45]
Centroid: CG[30; 15]
Coordinates of the circumscribed circle: U[22.5; 22.5]
Coordinates of the inscribed circle: I[31.82198051534; 13.18801948466]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 135° = 0.78553981634 rad

# How did we calculate this triangle?

### 1. Calculate the third unknown inner angle ### 2. By using the law of sines, we calculate unknown side a ### 3. By using the law of sines, we calculate last unknown side b 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. ### 4. The triangle circumference is the sum of the lengths of its three sides ### 5. Semiperimeter of the triangle ### 6. The triangle area using Heron's formula ### 7. Calculate the heights of the triangle from its area. ### 8. Calculation of the inner angles of the triangle using a Law of Cosines    