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 = 2.07108294825   b = 4.44109081565   c = 4.9

Area: T = 4.59881817698
Perimeter: p = 11.4121737639
Semiperimeter: s = 5.70658688195

Angle ∠ A = α = 25° = 0.4366332313 rad
Angle ∠ B = β = 65° = 1.13444640138 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 4.44109081565
Height: hb = 2.07108294825
Height: hc = 1.87768088856

Median: ma = 4.56600163312
Median: mb = 3.03662396248
Median: mc = 2.45

Inradius: r = 0.80658688195
Circumradius: R = 2.45

Vertex coordinates: A[4.9; 0] B[0; 0] C[0.87551703563; 1.87768088856]
Centroid: CG[1.92550567854; 0.62656029619]
Coordinates of the circumscribed circle: U[2.45; -0]
Coordinates of the inscribed circle: I[1.2654960663; 0.80658688195]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155° = 0.4366332313 rad
∠ B' = β' = 115° = 1.13444640138 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 = 4.9 ; ; alpha = 25° ; ;

2. From angle α we calculate angle β:

 alpha + beta + 90° = 180° ; ; beta = 90° - alpha = 90° - 25 ° = 65 ° ; ;

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

 sin alpha = a:c ; ; a = c * sin alpha = c * sin(25 ° ) = 2.071 ; ;

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{ 4.9**2 - 2.071**2 } = 4.441 ; ;


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 = 2.07 ; ; b = 4.44 ; ; c = 4.9 ; ;

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

p = a+b+c = 2.07+4.44+4.9 = 11.41 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.41 }{ 2 } = 5.71 ; ;

7. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.71 * (5.71-2.07)(5.71-4.44)(5.71-4.9) } ; ; T = sqrt{ 21.14 } = 4.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.6 }{ 2.07 } = 4.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.6 }{ 4.44 } = 2.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.6 }{ 4.9 } = 1.88 ; ;

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{ 2.07**2-4.44**2-4.9**2 }{ 2 * 4.44 * 4.9 } ) = 25° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.44**2-2.07**2-4.9**2 }{ 2 * 2.07 * 4.9 } ) = 65° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.9**2-2.07**2-4.44**2 }{ 2 * 4.44 * 2.07 } ) = 90° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.6 }{ 5.71 } = 0.81 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.07 }{ 2 * sin 25° } = 2.45 ; ;
Trigonometry right triangle solver. Find the hypotenuse c of a triangle - calculator. Area T of right triangle calculator.

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