Right triangle calculator

Please enter two properties of the right triangle

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


You have entered cathetus a, cathetus b and hypotenuse c.

Right scalene triangle.

Sides: a = 80   b = 90   c = 120.4165945788

Area: T = 3600
Perimeter: p = 290.4165945788
Semiperimeter: s = 145.2087972894

Angle ∠ A = α = 41.63435393366° = 41°38'1″ = 0.72766423407 rad
Angle ∠ B = β = 48.36664606634° = 48°21'59″ = 0.84441539861 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 90
Height: hb = 80
Height: hc = 59.79327454947

Median: ma = 98.4898578018
Median: mb = 91.78877987534
Median: mc = 60.2087972894

Inradius: r = 24.7922027106
Circumradius: R = 60.2087972894

Vertex coordinates: A[120.4165945788; 0] B[0; 0] C[53.14991071064; 59.79327454947]
Centroid: CG[57.85550176314; 19.93109151649]
Coordinates of the circumscribed circle: U[60.2087972894; 0]
Coordinates of the inscribed circle: I[55.2087972894; 24.7922027106]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.3666460663° = 138°21'59″ = 0.72766423407 rad
∠ B' = β' = 131.6343539337° = 131°38'1″ = 0.84441539861 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a cathetus b hypotenuse c

a = 80 ; ; b = 90 ; ; c = 120.416 ; ;


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 = 80 ; ; b = 90 ; ; c = 120.42 ; ;

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

p = a+b+c = 80+90+120.42 = 290.42 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 290.42 }{ 2 } = 145.21 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 145.21 * (145.21-80)(145.21-90)(145.21-120.42) } ; ; T = sqrt{ 12960000 } = 3600 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3600 }{ 80 } = 90 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3600 }{ 90 } = 80 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3600 }{ 120.42 } = 59.79 ; ;

6. 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{ 80**2-90**2-120.42**2 }{ 2 * 90 * 120.42 } ) = 41° 38'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 90**2-80**2-120.42**2 }{ 2 * 80 * 120.42 } ) = 48° 21'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 120.42**2-80**2-90**2 }{ 2 * 90 * 80 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3600 }{ 145.21 } = 24.79 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 80 }{ 2 * sin 41° 38'1" } = 60.21 ; ;
Trigonometry right triangle solver. Find the hypotenuse c of a triangle - calculator. Area T of right triangle calculator.

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