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 = 1077.984364002   b = 479.9499238829   c = 1180

Area: T = 258688.7143749
Perimeter: p = 2737.933287885
Semiperimeter: s = 1368.966643942

Angle ∠ A = α = 66° = 1.15219173063 rad
Angle ∠ B = β = 24° = 0.41988790205 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 479.9499238829
Height: hb = 1077.984364002
Height: hc = 438.4555447032

Median: ma = 721.7098704319
Median: mb = 1104.372156162
Median: mc = 590

Inradius: r = 188.9666439424
Circumradius: R = 590

Vertex coordinates: A[1180; 0] B[0; 0] C[984.7877057752; 438.4555447032]
Centroid: CG[721.5965685917; 146.1521815677]
Coordinates of the circumscribed circle: U[590; 0]
Coordinates of the inscribed circle: I[889.0177200594; 188.9666439424]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114° = 1.15219173063 rad
∠ B' = β' = 156° = 0.41988790205 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 = 1180 ; ; alpha = 66° ; ;

2. From angle α we calculate angle β:

alpha + beta + 90° = 180° ; ; beta = 90° - alpha = 90° - 66 ° = 24 ° ; ;

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

sin alpha = a:c ; ; a = c * sin alpha = 1180 * sin(66 ° ) = 1077.984 ; ;

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{ 1180**2 - 1077.984**2 } = 479.949 ; ;


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 = 1077.98 ; ; b = 479.95 ; ; c = 1180 ; ;

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

p = a+b+c = 1077.98+479.95+1180 = 2737.93 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2737.93 }{ 2 } = 1368.97 ; ;

7. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1368.97 * (1368.97-1077.98)(1368.97-479.95)(1368.97-1180) } ; ; T = sqrt{ 66919850620.9 } = 258688.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 258688.71 }{ 1077.98 } = 479.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 258688.71 }{ 479.95 } = 1077.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 258688.71 }{ 1180 } = 438.46 ; ;

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{ 1077.98**2-479.95**2-1180**2 }{ 2 * 479.95 * 1180 } ) = 66° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 479.95**2-1077.98**2-1180**2 }{ 2 * 1077.98 * 1180 } ) = 24° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1180**2-1077.98**2-479.95**2 }{ 2 * 479.95 * 1077.98 } ) = 90° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 258688.71 }{ 1368.97 } = 188.97 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1077.98 }{ 2 * sin 66° } = 590 ; ;
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