Right triangle calculator (B,b) - result

Please enter two properties of the right triangle

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


You have entered cathetus b and angle β.

Right scalene triangle.

Sides: a = 1351.683287848   b = 1175   c = 1790.997737688

Area: T = 794113.691111
Perimeter: p = 4317.688025536
Semiperimeter: s = 2158.844012768

Angle ∠ A = α = 49° = 0.85552113335 rad
Angle ∠ B = β = 41° = 0.71655849933 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 1175
Height: hb = 1351.683287848
Height: hc = 886.7843756762

Median: ma = 1355.502236112
Median: mb = 1473.839949397
Median: mc = 895.499868844

Inradius: r = 367.8432750803
Circumradius: R = 895.499868844

Vertex coordinates: A[1790.997737688; 0] B[0; 0] C[1020.128801782; 886.7843756762]
Centroid: CG[937.0421798232; 295.5954585587]
Coordinates of the circumscribed circle: U[895.499868844; -0]
Coordinates of the inscribed circle: I[983.8440127682; 367.8432750803]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131° = 0.85552113335 rad
∠ B' = β' = 139° = 0.71655849933 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus b and angle β

b = 1175 ; ; beta = 41° ; ;

2. From angle β we calculate angle α:

 alpha + beta + 90° = 180° ; ; alpha = 90° - beta = 90° - 41 ° = 49 ° ; ;

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

 cos alpha = b:c ; ; c = b/ cos alpha = 1175/ cos(49 ° ) = 1790.997 ; ;

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

 sin alpha = a:c ; ; a = c * sin alpha = 1790.997 * sin(49 ° ) = 1351.683 ; ;
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 = 1351.68 ; ; b = 1175 ; ; c = 1791 ; ;

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

p = a+b+c = 1351.68+1175+1791 = 4317.68 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4317.68 }{ 2 } = 2158.84 ; ;

7. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 1351.68 * 1175 }{ 2 } = 794113.69 ; ;

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

h _a = b = 1175 ; ; h _b = a = 1351.68 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 794113.69 }{ 1791 } = 886.78 ; ;

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{ 1351.68 }{ 1791 } ) = 49° ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 1175 }{ 1791 } ) = 41° ; ; gamma = 90° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 794113.69 }{ 2158.84 } = 367.84 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1351.68 }{ 2 * sin 49° } = 895.5 ; ;

12. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1175**2+2 * 1791**2 - 1351.68**2 } }{ 2 } = 1355.502 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1791**2+2 * 1351.68**2 - 1175**2 } }{ 2 } = 1473.839 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1175**2+2 * 1351.68**2 - 1791**2 } }{ 2 } = 895.499 ; ;
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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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