# Right triangle calculator (A,a)

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 angle α.

### Right scalene triangle.

Sides: a = 36   b = 20.78546096908   c = 41.56992193817

Area: T = 374.1232974435
Perimeter: p = 98.35438290725
Semiperimeter: s = 49.17769145362

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 20.78546096908
Height: hb = 36
Height: hc = 18

Median: ma = 27.49554541697
Median: mb = 37.47699879904
Median: mc = 20.78546096908

Inradius: r = 7.60876951546
Circumradius: R = 20.78546096908

Vertex coordinates: A[41.56992193817; 0] B[0; 0] C[31.17769145362; 18]
Centroid: CG[24.2498711306; 6]
Coordinates of the circumscribed circle: U[20.78546096908; 0]
Coordinates of the inscribed circle: I[28.39223048454; 7.60876951546]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 90° = 1.57107963268 rad

# How did we calculate this triangle?

### 1. Input data entered: cathetus a and angle α ### 2. From angle α we calculate angle β: ### 3. From cathetus a and angle α we calculate hypotenuse c: ### 4. From cathetus a and hypotenuse c we calculate cathetus b - Pythagorean theorem: 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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