# Triangle calculator

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

Triangle has two solutions: a=8.55; b=8.56; c=14.72985480637 and a=8.55; b=8.56; c=8.70875870329.

### #1 Obtuse scalene triangle.

Sides: a = 8.55   b = 8.56   c = 14.72985480637

Area: T = 32.06325
Perimeter: p = 31.83985480637
Semiperimeter: s = 15.91992740318

Angle ∠ A = α = 30.57219712649° = 30°34'19″ = 0.53435815574 rad
Angle ∠ B = β = 30.61215662609° = 30°36'42″ = 0.53442726204 rad
Angle ∠ C = γ = 118.8166462474° = 118°48'59″ = 2.07437384757 rad

Height: ha = 7.5
Height: hb = 7.49112383178
Height: hc = 4.35437896419

Median: ma = 11.26217156345
Median: mb = 11.25660167924
Median: mc = 4.35437935165

Inradius: r = 2.01440679742
Circumradius: R = 8.40550914283

Vertex coordinates: A[14.72985480637; 0] B[0; 0] C[7.35884655842; 4.35437896419]
Centroid: CG[7.36223378826; 1.4511263214]
Coordinates of the circumscribed circle: U[7.36442740318; -4.05112997794]
Coordinates of the inscribed circle: I[7.35992740318; 2.01440679742]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.4288028735° = 149°25'41″ = 0.53435815574 rad
∠ B' = β' = 149.3888433739° = 149°23'18″ = 0.53442726204 rad
∠ C' = γ' = 61.18435375258° = 61°11'1″ = 2.07437384757 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and height ha. ### 2. From side a we calculate T: 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 Acute scalene triangle.

Sides: a = 8.55   b = 8.56   c = 8.70875870329

Area: T = 32.06325
Perimeter: p = 25.81875870329
Semiperimeter: s = 12.90987935165

Angle ∠ A = α = 59.35215897327° = 59°21'6″ = 1.03658806571 rad
Angle ∠ B = β = 59.46548727416° = 59°27'54″ = 1.03878578186 rad
Angle ∠ C = γ = 61.18435375258° = 61°11'1″ = 1.06878541778 rad

Height: ha = 7.5
Height: hb = 7.49112383178
Height: hc = 7.36442674782

Median: ma = 7.50114805851
Median: mb = 7.49329223917
Median: mc = 7.36442740318

Inradius: r = 2.48437720085
Circumradius: R = 4.96991296668

Vertex coordinates: A[8.70875870329; 0] B[0; 0] C[4.34439687511; 7.36442674782]
Centroid: CG[4.35105185947; 2.45547558261]
Coordinates of the circumscribed circle: U[4.35437935165; 2.39551475239]
Coordinates of the inscribed circle: I[4.34987935165; 2.48437720085]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.6488410267° = 120°38'54″ = 1.03658806571 rad
∠ B' = β' = 120.5355127258° = 120°32'6″ = 1.03878578186 rad
∠ C' = γ' = 118.8166462474° = 118°48'59″ = 1.06878541778 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and height ha. ### 2. From side a we calculate T: 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    