# Right triangle calculator (S,b)

Please enter two properties of the right triangle

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

You have entered cathetus b and area S.

### Right scalene Pythagorean triangle.

Sides: a = 36   b = 48   c = 60

Area: T = 864
Perimeter: p = 144
Semiperimeter: s = 72

Angle ∠ A = α = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 48
Height: hb = 36
Height: hc = 28.8

Median: ma = 51.26440224719
Median: mb = 43.26766153056
Median: mc = 30

Inradius: r = 12
Circumradius: R = 30

Vertex coordinates: A[60; 0] B[0; 0] C[21.6; 28.8]
Centroid: CG[27.2; 9.6]
Coordinates of the circumscribed circle: U[30; 0]
Coordinates of the inscribed circle: I[24; 12]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 90° = 1.57107963268 rad

# How did we calculate this triangle?

### 1. Input data entered: cathetus b and area S ### 2. From area S and cathetus b we calculate cathetus a: ### 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   ### 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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