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 = 3.84877266124   b = 10.57215419838   c = 11.25

Area: T = 20.33882017127
Perimeter: p = 25.66992685963
Semiperimeter: s = 12.83546342981

Angle ∠ A = α = 20° = 0.34990658504 rad
Angle ∠ B = β = 70° = 1.22217304764 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 10.57215419838
Height: hb = 3.84877266124
Height: hc = 3.61656803045

Median: ma = 10.74551733321
Median: mb = 6.53879182515
Median: mc = 5.625

Inradius: r = 1.58546342981
Circumradius: R = 5.625

Vertex coordinates: A[11.25; 0] B[0; 0] C[1.31660000075; 3.61656803045]
Centroid: CG[4.18986666692; 1.20552267682]
Coordinates of the circumscribed circle: U[5.625; -0]
Coordinates of the inscribed circle: I[2.26330923143; 1.58546342981]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160° = 0.34990658504 rad
∠ B' = β' = 110° = 1.22217304764 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 = 11.25 ; ; alpha = 20° ; ;

2. From angle α we calculate angle β:

 alpha + beta + 90° = 180° ; ; beta = 90° - alpha = 90° - 20 ° = 70 ° ; ;

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

 sin alpha = a:c ; ; a = c * sin alpha = c * sin(20 ° ) = 3.848 ; ;

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{ 11.25**2 - 3.848**2 } = 10.572 ; ;


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 = 3.85 ; ; b = 10.57 ; ; c = 11.25 ; ;

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

p = a+b+c = 3.85+10.57+11.25 = 25.67 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25.67 }{ 2 } = 12.83 ; ;

7. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.83 * (12.83-3.85)(12.83-10.57)(12.83-11.25) } ; ; T = sqrt{ 413.64 } = 20.34 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20.34 }{ 3.85 } = 10.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20.34 }{ 10.57 } = 3.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20.34 }{ 11.25 } = 3.62 ; ;

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{ 3.85**2-10.57**2-11.25**2 }{ 2 * 10.57 * 11.25 } ) = 20° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10.57**2-3.85**2-11.25**2 }{ 2 * 3.85 * 11.25 } ) = 70° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11.25**2-3.85**2-10.57**2 }{ 2 * 10.57 * 3.85 } ) = 90° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20.34 }{ 12.83 } = 1.58 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.85 }{ 2 * sin 20° } = 5.63 ; ;
Trigonometry right triangle solver. Find the hypotenuse c of a triangle - calculator. Area T of right triangle calculator.

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