Right triangle calculator (b,p)
You have entered cathetus b and perimeter p.Right scalene triangle.
The lengths of the sides of the triangle:a = 4.26547058824
b = 12
c = 12.73552941176
Area: T = 25.58882352941
Perimeter: p = 29
Semiperimeter: s = 14.5
Angle ∠ A = α = 19.56548140636° = 19°33'53″ = 0.3411470423 rad
Angle ∠ B = β = 70.43551859364° = 70°26'7″ = 1.22993259038 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad
Altitude (height) to the side a: ha = 12
Altitude (height) to the side b: hb = 4.26547058824
Altitude (height) to the side c: hc = 4.01884757506
Median: ma = 12.18879829777
Median: mb = 7.36112306215
Median: mc = 6.36876470588
Line segment ca = 11.30771593533
Line segment cb = 1.42881347643
Inradius: r = 1.76547058824
Circumradius: R = 6.36876470588
Vertex coordinates: A[12.73552941176; 0] B[0; 0] C[1.42881347643; 4.01884757506]
Centroid: CG[4.72111429606; 1.33994919169]
Coordinates of the circumscribed circle: U[6.36876470588; -0]
Coordinates of the inscribed circle: I[2.5; 1.76547058824]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 160.43551859364° = 160°26'7″ = 0.3411470423 rad
∠ B' = β' = 109.56548140636° = 109°33'53″ = 1.22993259038 rad
∠ C' = γ' = 90° = 1.57107963268 rad
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How did we calculate this triangle?
The calculation of the triangle has two phases. The first phase calculates all three sides of the triangle from the input parameters. The first phase is different for the different triangles query entered. The second phase calculates other triangle characteristics, such as angles, area, perimeter, heights, the center of gravity, circle radii, etc. Some input data also results in two to three correct triangle solutions (e.g., if the specified triangle area and two sides - typically resulting in both acute and obtuse) triangle).1. Input data entered: cathetus b and perimeter p
2. From the cathetus b, we calculate hypotenuse c - Pythagorean theorem:
We know the lengths of all three sides of the triangle, so the triangle is uniquely specified. Next, we calculate another of its characteristics - the same procedure for calculating the triangle from the known three sides SSS.
3. The triangle perimeter is the sum of the lengths of its three sides
4. Semiperimeter of the triangle
The semiperimeter of the triangle is half its perimeter. The semiperimeter frequently appears in formulas for triangles to be given a separate name. By the triangle inequality, the longest side length of a triangle is less than the semiperimeter.s=2p=229=14.5
5. The triangle area - from two legs
6. Calculate the heights of the right triangle from its area.
7. Calculation of the inner angles of the triangle - basic use of sine function
8. Inradius
An incircle of a triangle is a tangent circle to each side. An incircle center is called an incenter and has a radius named inradius. All triangles have an incenter, and it always lies inside the triangle. The incenter is the intersection of the three-angle bisectors. The product of a triangle's inradius and semiperimeter (half the perimeter) is its area.9. Circumradius
The circumcircle of a triangle is a circle that passes through all of the triangle's vertices, and the circumradius of a triangle is the radius of the triangle's circumcircle. The circumcenter (center of the circumcircle) is the point where the perpendicular bisectors of a triangle intersect.10. Calculation of medians
A median of a triangle is a line segment joining a vertex to the opposite side's midpoint. Every triangle has three medians, and they all intersect each other at the triangle's centroid. The centroid divides each median into parts in the ratio of 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex. We use Apollonius's theorem to calculate a median's length from its side's lengths.Calculate another triangle
Look also at our friend's collection of math problems and questions:
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