# Right triangle calculator - result

Please enter two properties of the right triangle

Use symbols: a, b, c, A, B, h, T, p, r, R

You have entered cathetus a and area S.

### Right scalene triangle.

Sides: a = 12   b = 5   c = 13

Area: T = 30
Perimeter: p = 30
Semiperimeter: s = 15

Angle ∠ A = α = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ B = β = 22.6219864948° = 22°37'11″ = 0.39547911197 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 5
Height: hb = 12
Height: hc = 4.61553846154

Median: ma = 7.81102496759
Median: mb = 12.25876506721
Median: mc = 6.5

Inradius: r = 2
Circumradius: R = 6.5

Vertex coordinates: A[13; 0] B[0; 0] C[11.07769230769; 4.61553846154]
Centroid: CG[8.02656410256; 1.53884615385]
Coordinates of the circumscribed circle: U[6.5; -0]
Coordinates of the inscribed circle: I[10; 2]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad
∠ B' = β' = 157.3880135052° = 157°22'49″ = 0.39547911197 rad
∠ C' = γ' = 90° = 1.57107963268 rad

# How did we calculate this triangle?

### 1. Input data entered: cathetus a and area S ### 2. From area S and cathetus a we calculate cathetus b: ### 3. From cathetus a and cathetus b we calculate hypotenuse c - Pythagorean theorem: ### 4. From area S and hypotenuse c we calculate height h: 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. ### 5. The triangle circumference is the sum of the lengths of its three sides ### 6. Semiperimeter of the triangle ### 7. The triangle area - from two legs ### 8. Calculate the heights of the triangle from its area. ### 9. Calculation of the inner angles of the triangle - basic use of sine function ### 10. Inradius ### 11. Circumradius ### 12. Calculation of medians Trigonometry right triangle solver. You can calculate angles, sides (adjacent, opposite, hypotenuse) and area of any right-angled triangle and use it in real world to find height. A right-angled triangle is entirely determined by two independent properties. Step-by-step explanations are provided for each calculation.

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