Right triangle calculator (S,r) - result

Please enter two properties of the right triangle

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

You have entered area S and inradius r.

Right scalene Pythagorean triangle.

Sides: a = 20   b = 15   c = 25

Area: T = 150
Perimeter: p = 60
Semiperimeter: s = 30

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

Height: ha = 15
Height: hb = 20
Height: hc = 12

Median: ma = 18.02877563773
Median: mb = 21.36600093633
Median: mc = 12.5

Inradius: r = 5
Circumradius: R = 12.5

Vertex coordinates: A[25; 0] B[0; 0] C[16; 12]
Centroid: CG[13.66766666667; 4]
Coordinates of the circumscribed circle: U[12.5; -0]
Coordinates of the inscribed circle: I[15; 5]

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

How did we calculate this triangle?

1. Input data entered: area S and inradius r 2. From area S and inradius r we calculate hypotenuse c: 3. From area S and hypotenuse c we calculate height h: 4. From hypotenuse c and height h we calculate a,b - Pythagorean theorem, Euclid's 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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