# Triangle calculator

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

Triangle has two solutions: a=37; b=34; c=3.60107197786 and a=37; b=34; c=59.1554839337.

### #1 Obtuse scalene triangle.

Sides: a = 37   b = 34   c = 3.60107197786

Area: T = 35.32996793519
Perimeter: p = 74.60107197786
Semiperimeter: s = 37.33003598893

Angle ∠ A = α = 144.7832852456° = 144°46'58″ = 2.52769374758 rad
Angle ∠ B = β = 32° = 0.55985053606 rad
Angle ∠ C = γ = 3.21771475437° = 3°13'2″ = 0.05661498172 rad

Height: ha = 1.90880907758
Height: hb = 2.07664517266
Height: hc = 19.60770127766

Median: ma = 15.56438231634
Median: mb = 20.05495035216
Median: mc = 35.48660353417

Inradius: r = 0.94663629696
Circumradius: R = 32.08803585516

Vertex coordinates: A[3.60107197786; 0] B[0; 0] C[31.37877795578; 19.60770127766]
Centroid: CG[11.65994997788; 6.53656709255]
Coordinates of the circumscribed circle: U[1.88003598893; 32.03298003283]
Coordinates of the inscribed circle: I[3.33003598893; 0.94663629696]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 35.21771475437° = 35°13'2″ = 2.52769374758 rad
∠ B' = β' = 148° = 0.55985053606 rad
∠ C' = γ' = 176.7832852456° = 176°46'58″ = 0.05661498172 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle β. ### 2. From angle β, side a and side b 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   ### 10. Calculation of medians ### #2 Obtuse scalene triangle.

Sides: a = 37   b = 34   c = 59.1554839337

Area: T = 579.925484534
Perimeter: p = 130.1554839337
Semiperimeter: s = 65.07774196685

Angle ∠ A = α = 35.21771475437° = 35°13'2″ = 0.61546551778 rad
Angle ∠ B = β = 32° = 0.55985053606 rad
Angle ∠ C = γ = 112.7832852456° = 112°46'58″ = 1.96884321152 rad

Height: ha = 31.34772889373
Height: hb = 34.11332261965
Height: hc = 19.60770127766

Median: ma = 44.5587799637
Median: mb = 46.3165737158
Median: mc = 19.68994958227

Inradius: r = 8.91113066912
Circumradius: R = 32.08803585516

Vertex coordinates: A[59.1554839337; 0] B[0; 0] C[31.37877795578; 19.60770127766]
Centroid: CG[30.17875396316; 6.53656709255]
Coordinates of the circumscribed circle: U[29.57774196685; -12.42327875516]
Coordinates of the inscribed circle: I[31.07774196685; 8.91113066912]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.7832852456° = 144°46'58″ = 0.61546551778 rad
∠ B' = β' = 148° = 0.55985053606 rad
∠ C' = γ' = 67.21771475437° = 67°13'2″ = 1.96884321152 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle β. ### 2. From angle β, side a and side b 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    