Right triangle calculator (A)

Please enter two properties of the right triangle

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


You have entered area T and angle α.

Right scalene triangle.

Sides: a = 55.0000297247   b = 76.9999583856   c = 8.60223086813

Area: T = 17.5
Perimeter: p = 20.60222967917
Semiperimeter: s = 10.30111483958

Angle ∠ A = α = 35.538° = 35°32'17″ = 0.62202551096 rad
Angle ∠ B = β = 54.462° = 54°27'43″ = 0.95105412172 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 76.9999583856
Height: hb = 55.0000297247
Height: hc = 4.06986752006

Median: ma = 7.43330001825
Median: mb = 6.10332902273
Median: mc = 4.30111543407

Inradius: r = 1.69988397145
Circumradius: R = 4.30111543407

Vertex coordinates: A[8.60223086813; 0] B[0; 0] C[2.90662311264; 4.06986752006]
Centroid: CG[3.83661799359; 1.35662250669]
Coordinates of the circumscribed circle: U[4.30111543407; 0]
Coordinates of the inscribed circle: I[3.30111900102; 1.69988397145]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.462° = 144°27'43″ = 0.62202551096 rad
∠ B' = β' = 125.538° = 125°32'17″ = 0.95105412172 rad
∠ C' = γ' = 90° = 1.57107963268 rad

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: angle α and area T

 alpha = 35.538° ; ; S = 17.5 ; ;

2. From angle α we calculate angle β:

 alpha + beta + 90° = 180° ; ; beta = 90° - alpha = 90° - 35.538 ° = 54.462 ° ; ;

3. From area T, angle α and angle β we calculate hypotenuse c:

c**2 sin alpha sin beta = 2 S ; ; c = sqrt{ fraction{ 2 S }{ sin alpha sin beta } } ; ; c = sqrt{ fraction{ 2 * 17.5 }{ sin 35° 32'17" * sin 54° 27'43" } } = 8.602 ; ;

4. From area T and hypotenuse c we calculate height h:

S = fraction{ c * h }{ 2 } ; ; h = 2 * S / c = 2 * 17.5 / 8.602 = 4.069 ; ;

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

 sin alpha = a:c ; ; a = c * sin alpha = 8.602 * sin(35.538 ° ) = 5 ; ;

6. 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{ 8.602**2 - 5**2 } = 7 ; ;
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 = 5 ; ; b = 7 ; ; c = 8.6 ; ;

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

p = a+b+c = 5+7+8.6 = 20.6 ; ;

8. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20.6 }{ 2 } = 10.3 ; ;

9. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 5 * 7 }{ 2 } = 17.5 ; ;

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

h _a = b = 7 ; ; h _b = a = 5 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.5 }{ 8.6 } = 4.07 ; ;

11. 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{ 5 }{ 8.6 } ) = 35° 32'17" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 7 }{ 8.6 } ) = 54° 27'43" ; ; gamma = 90° ; ;

12. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.5 }{ 10.3 } = 1.7 ; ;

13. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5 }{ 2 * sin 35° 32'17" } = 4.3 ; ;

14. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7**2+2 * 8.6**2 - 5**2 } }{ 2 } = 7.433 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.6**2+2 * 5**2 - 7**2 } }{ 2 } = 6.103 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7**2+2 * 5**2 - 8.6**2 } }{ 2 } = 4.301 ; ;
Calculate another triangle

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.

Calculate right triangle by:

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.