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 and 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 - from two legs

T = fraction{ ab }{ 2 } = fraction{ 80 * 90 }{ 2 } = 3600 ; ;

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

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

6. 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{ 80 }{ 120.42 } ) = 41° 38'1" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 90 }{ 120.42 } ) = 48° 21'59" ; ; gamma = 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 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 120.42**2 - 80**2 } }{ 2 } = 98.489 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 120.42**2+2 * 80**2 - 90**2 } }{ 2 } = 91.788 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 80**2 - 120.42**2 } }{ 2 } = 60.208 ; ;
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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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