Right triangle calculator (A,c)

Please enter two properties of the right triangle

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


You have entered hypotenuse c and angle α.

Right scalene triangle.

Sides: a = 197.5166106277   b = 929.2440220697   c = 950

Area: T = 91769.9555094
Perimeter: p = 2076.756632697
Semiperimeter: s = 1038.378816349

Angle ∠ A = α = 12° = 0.20994395102 rad
Angle ∠ B = β = 78° = 1.36113568166 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 929.2440220697
Height: hb = 197.5166106277
Height: hc = 193.2199905461

Median: ma = 934.473340295
Median: mb = 504.8610831496
Median: mc = 475

Inradius: r = 88.3788163487
Circumradius: R = 475

Vertex coordinates: A[950; 0] B[0; 0] C[41.06659076198; 193.2199905461]
Centroid: CG[330.355530254; 64.4399968487]
Coordinates of the circumscribed circle: U[475; 0]
Coordinates of the inscribed circle: I[109.138794279; 88.3788163487]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168° = 0.20994395102 rad
∠ B' = β' = 102° = 1.36113568166 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: hypotenuse c angle α

c = 950 ; ; alpha = 12° ; ;

2. From angle α we calculate angle β:

 alpha + beta + 90° = 180° ; ; beta = 90° - alpha = 90° - 12 ° = 78 ° ; ;

3. From hypotenuse c and angle α we calculate cathetus a:

 sin alpha = a:c ; ; a = c * sin alpha = c * sin(12 ° ) = 197.516 ; ;

4. From cathetus a and hypotenuse c we calculate cathetus b - Pythagorean theorem:

c**2 = a**2+b**2 ; ; b = sqrt{ c**2 - a**2 } = sqrt{ 950**2 - 197.516**2 } = 929.24 ; ;


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.

a = 197.52 ; ; b = 929.24 ; ; c = 950 ; ;

5. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 197.52+929.24+950 = 2076.76 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2076.76 }{ 2 } = 1038.38 ; ;

7. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1038.38 * (1038.38-197.52)(1038.38-929.24)(1038.38-950) } ; ; T = sqrt{ 8421724657.95 } = 91769.96 ; ;

8. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 91769.96 }{ 197.52 } = 929.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 91769.96 }{ 929.24 } = 197.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 91769.96 }{ 950 } = 193.2 ; ;

9. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 197.52**2-929.24**2-950**2 }{ 2 * 929.24 * 950 } ) = 12° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 929.24**2-197.52**2-950**2 }{ 2 * 197.52 * 950 } ) = 78° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 950**2-197.52**2-929.24**2 }{ 2 * 929.24 * 197.52 } ) = 90° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 91769.96 }{ 1038.38 } = 88.38 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 197.52 }{ 2 * sin 12° } = 475 ; ;
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