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 = 74.51437816936   b = 433.6454665986   c = 440

Area: T = 16156.25219869
Perimeter: p = 948.1588447679
Semiperimeter: s = 474.079922384

Angle ∠ A = α = 9.75° = 9°45' = 0.17701696021 rad
Angle ∠ B = β = 80.25° = 80°15' = 1.40106267247 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 433.6454665986
Height: hb = 74.51437816936
Height: hc = 73.43875090314

Median: ma = 435.2422199532
Median: mb = 229.2698898342
Median: mc = 220

Inradius: r = 34.07992238396
Circumradius: R = 220

Vertex coordinates: A[440; 0] B[0; 0] C[12.61988719597; 73.43875090314]
Centroid: CG[150.873295732; 24.47991696771]
Coordinates of the circumscribed circle: U[220; 0]
Coordinates of the inscribed circle: I[40.4354557854; 34.07992238396]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.25° = 170°15' = 0.17701696021 rad
∠ B' = β' = 99.75° = 99°45' = 1.40106267247 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 = 440 ; ; alpha = 9.75° ; ;

2. From angle α we calculate angle β:

 alpha + beta + 90° = 180° ; ; beta = 90° - alpha = 90° - 9.75 ° = 80.25 ° ; ;

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

 sin alpha = a:c ; ; a = c * sin alpha = 440 * sin(9.75 ° ) = 74.514 ; ;

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{ 440**2 - 74.514**2 } = 433.645 ; ;
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 = 74.51 ; ; b = 433.64 ; ; c = 440 ; ;

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

p = a+b+c = 74.51+433.64+440 = 948.16 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 948.16 }{ 2 } = 474.08 ; ;

7. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 74.51 * 433.64 }{ 2 } = 16156.25 ; ;

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

h _a = b = 433.64 ; ; h _b = a = 74.51 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16156.25 }{ 440 } = 73.44 ; ;

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{ 74.51 }{ 440 } ) = 9° 45' ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 433.64 }{ 440 } ) = 80° 15' ; ; gamma = 90° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16156.25 }{ 474.08 } = 34.08 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 74.51 }{ 2 * sin 9° 45' } = 220 ; ;

12. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 433.64**2+2 * 440**2 - 74.51**2 } }{ 2 } = 435.242 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 440**2+2 * 74.51**2 - 433.64**2 } }{ 2 } = 229.269 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 433.64**2+2 * 74.51**2 - 440**2 } }{ 2 } = 220 ; ;
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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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