Right triangle calculator (B,a)

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 and angle β.

Right scalene triangle.

Sides: a = 150   b = 40.19223788647   c = 155.2911427062

Area: T = 3014.428841485
Perimeter: p = 345.4843805926
Semiperimeter: s = 172.7421902963

Angle ∠ A = α = 75° = 1.3098996939 rad
Angle ∠ B = β = 15° = 0.26217993878 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 40.19223788647
Height: hb = 150
Height: hc = 38.82328567654

Median: ma = 85.09107005424
Median: mb = 151.3440202292
Median: mc = 77.64657135308

Inradius: r = 17.45504759016
Circumradius: R = 77.64657135308

Vertex coordinates: A[155.2911427062; 0] B[0; 0] C[144.8898873943; 38.82328567654]
Centroid: CG[100.0660100335; 12.94109522551]
Coordinates of the circumscribed circle: U[77.64657135308; -0]
Coordinates of the inscribed circle: I[132.5549524098; 17.45504759016]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105° = 1.3098996939 rad
∠ B' = β' = 165° = 0.26217993878 rad
∠ C' = γ' = 90° = 1.57107963268 rad

How did we calculate this triangle?

1. Input data entered: cathetus a and angle β 2. From angle β we calculate angle α: 3. From cathetus a and angle α we calculate hypotenuse c: 4. From cathetus a and hypotenuse c we calculate cathetus b - Pythagorean theorem: 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. 5. The triangle circumference is the sum of the lengths of its three sides 6. Semiperimeter of the triangle 7. The triangle area - from two legs 8. Calculate the heights of the triangle from its area. 9. Calculation of the inner angles of the triangle - basic use of sine function   12. Calculation of medians 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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