# Triangle calculator - result

Please enter what you know about the triangle:
You have entered side a, b and angle α.

Triangle has two solutions: a=13; b=14; c=2.21113544315 and a=13; b=14; c=12.2109711666.

### #1 Obtuse scalene triangle.

Sides: a = 13   b = 14   c = 2.21113544315

Area: T = 13.26985049627
Perimeter: p = 29.21113544315
Semiperimeter: s = 14.60656772158

Angle ∠ A = α = 59° = 1.03297442587 rad
Angle ∠ B = β = 112.616594319° = 112°36'57″ = 1.96655189989 rad
Angle ∠ C = γ = 8.38440568099° = 8°23'3″ = 0.1466329396 rad

Height: ha = 2.04113084558
Height: hb = 1.8965500709
Height: hc = 122.0003422098

Median: ma = 7.62985676382
Median: mb = 6.16599548871
Median: mc = 13.46439324825

Inradius: r = 0.90884484592
Circumradius: R = 7.58331170819

Vertex coordinates: A[2.21113544315; 0] B[0; 0] C[-4.99991786172; 122.0003422098]
Centroid: CG[-0.92992747286; 44.0001140699]
Coordinates of the circumscribed circle: U[1.10656772158; 7.50220758842]
Coordinates of the inscribed circle: I[0.60656772158; 0.90884484592]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121° = 1.03297442587 rad
∠ B' = β' = 67.38440568099° = 67°23'3″ = 1.96655189989 rad
∠ C' = γ' = 171.616594319° = 171°36'57″ = 0.1466329396 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle α. ### 2. From angle α, side b and side a we calculate side c - by using the law of cosines and quadratic equation:  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. ### 3. The triangle circumference is the sum of the lengths of its three sides ### 4. Semiperimeter of the triangle ### 5. The triangle area using Heron's formula ### 6. Calculate the heights of the triangle from its area. ### 7. Calculation of the inner angles of the triangle using a Law of Cosines ### 8. Inradius ### 9. Circumradius ### 10. Calculation of medians ### #2 Acute scalene triangle.

Sides: a = 13   b = 14   c = 12.2109711666

Area: T = 73.26603591375
Perimeter: p = 39.2109711666
Semiperimeter: s = 19.6054855833

Angle ∠ A = α = 59° = 1.03297442587 rad
Angle ∠ B = β = 67.38440568099° = 67°23'3″ = 1.17660736547 rad
Angle ∠ C = γ = 53.61659431901° = 53°36'57″ = 0.93657747402 rad

Height: ha = 11.27108244827
Height: hb = 10.46657655911
Height: hc = 122.0003422098

Median: ma = 11.4144400093
Median: mb = 10.49899251419
Median: mc = 12.05111715305

Inradius: r = 3.73768476342
Circumradius: R = 7.58331170819

Vertex coordinates: A[12.2109711666; 0] B[0; 0] C[4.99991786172; 122.0003422098]
Centroid: CG[5.73662967611; 44.0001140699]
Coordinates of the circumscribed circle: U[6.1054855833; 4.49882663256]
Coordinates of the inscribed circle: I[5.6054855833; 3.73768476342]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121° = 1.03297442587 rad
∠ B' = β' = 112.616594319° = 112°36'57″ = 1.17660736547 rad
∠ C' = γ' = 126.384405681° = 126°23'3″ = 0.93657747402 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle α. ### 2. From angle α, side b and side a we calculate side c - by using the law of cosines and quadratic equation:  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. ### 3. The triangle circumference is the sum of the lengths of its three sides ### 4. Semiperimeter of the triangle ### 5. The triangle area using Heron's formula ### 6. Calculate the heights of the triangle from its area. ### 7. Calculation of the inner angles of the triangle using a Law of Cosines ### 8. Inradius ### 9. Circumradius ### 10. Calculation of medians #### Look also our friend's collection of math examples and problems:

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