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 and 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 = 950 * 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 - from two legs

T = fraction{ ab }{ 2 } = fraction{ 197.52 * 929.24 }{ 2 } = 91769.96 ; ;

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

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

9. Calculation of the inner angles of the triangle - basic use of sine function

 sin alpha = fraction{ a }{ c } ; ; alpha = arcsin( fraction{ a }{ c } ) = arcsin( fraction{ 197.52 }{ 950 } ) = 12° ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 929.24 }{ 950 } ) = 78° ; ; gamma = 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 ; ;

12. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 929.24**2+2 * 950**2 - 197.52**2 } }{ 2 } = 934.473 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 950**2+2 * 197.52**2 - 929.24**2 } }{ 2 } = 504.861 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 929.24**2+2 * 197.52**2 - 950**2 } }{ 2 } = 475 ; ;
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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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