Right triangle calculator (B,b)

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 = 426.0439519005   b = 345   c = 548.2110426528

Area: T = 73491.81770283
Perimeter: p = 1319.254994553
Semiperimeter: s = 659.6254972766

Angle ∠ A = α = 51° = 0.89901179185 rad
Angle ∠ B = β = 39° = 0.68106784083 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 345
Height: hb = 426.0439519005
Height: hc = 268.1155356703

Median: ma = 405.4665680346
Median: mb = 459.6376728029
Median: mc = 274.1055213264

Inradius: r = 111.4154546238
Circumradius: R = 274.1055213264

Vertex coordinates: A[548.2110426528; 0] B[0; 0] C[331.0954891615; 268.1155356703]
Centroid: CG[293.1021772714; 89.37217855676]
Coordinates of the circumscribed circle: U[274.1055213264; 0]
Coordinates of the inscribed circle: I[314.6254972766; 111.4154546238]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129° = 0.89901179185 rad
∠ B' = β' = 141° = 0.68106784083 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 = 345 ; ; beta = 39° ; ;

2. From angle β we calculate angle α:

 alpha + beta + 90° = 180° ; ; alpha = 90° - beta = 90° - 39 ° = 51 ° ; ;

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

 cos alpha = b:c ; ; c = b/ cos alpha = 345/ cos(51 ° ) = 548.21 ; ;

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

 sin alpha = a:c ; ; a = c * sin alpha = 548.21 * sin(51 ° ) = 426.04 ; ;


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 = 426.04 ; ; b = 345 ; ; c = 548.21 ; ;

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

p = a+b+c = 426.04+345+548.21 = 1319.25 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1319.25 }{ 2 } = 659.62 ; ;

7. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 426.04 * 345 }{ 2 } = 73491.82 ; ;

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

h _a = b = 345 ; ; h _b = a = 426.04 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 73491.82 }{ 548.21 } = 268.12 ; ;

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{ 426.04 }{ 548.21 } ) = 51° ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 345 }{ 548.21 } ) = 39° ; ; gamma = 90° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 73491.82 }{ 659.62 } = 111.41 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 426.04 }{ 2 * sin 51° } = 274.11 ; ;

12. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 345**2+2 * 548.21**2 - 426.04**2 } }{ 2 } = 405.466 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 548.21**2+2 * 426.04**2 - 345**2 } }{ 2 } = 459.637 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 345**2+2 * 426.04**2 - 548.21**2 } }{ 2 } = 274.105 ; ;
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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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