Right triangle calculator - the result
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Right scalene triangle.
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a = 4.12112161292
b = 1.5
c = 4.38657066002
Area: T = 3.09109120969
Perimeter: p = 10.00769227294
Semiperimeter: s = 5.00334613647
Angle ∠ A = α = 70° = 1.22217304764 rad
Angle ∠ B = β = 20° = 0.34990658504 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad
Altitude (height) to the side a: ha = 1.5
Altitude (height) to the side b: hb = 4.12112161292
Altitude (height) to the side c: hc = 1.41095389312
Median: ma = 2.54987458869
Median: mb = 4.18989046759
Median: mc = 2.19328533001
Line segment ca = 0.5133030215
Line segment cb = 3.87326763853
Inradius: r = 0.61877547645
Circumradius: R = 2.19328533001
Vertex coordinates: A[4.38657066002; 0] B[0; 0] C[3.87326763853; 1.41095389312]
Centroid: CG[2.75327943285; 0.47698463104]
Coordinates of the circumscribed circle: U[2.19328533001; 0]
Coordinates of the inscribed circle: I[3.50334613647; 0.61877547645]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 110° = 1.22217304764 rad
∠ B' = β' = 160° = 0.34990658504 rad
∠ C' = γ' = 90° = 1.57107963268 rad
Calculate another triangle
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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 angle α
b=1.5 α=70°
2. From the angle α, we calculate angle β:
α+β+90°=180° β=90°−α=90°−70°=20°
3. From the cathetus b and angle α, we calculate hypotenuse c:
cosα=b:c c=b/cosα=1.5/cos(70°)=4.386
4. From the hypotenuse c and angle α, we calculate cathetus a:
sinα=a:c a=c⋅ sinα=4.386⋅ sin(70°)=4.121
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).
5. The triangle perimeter is the sum of the lengths of its three sides
6. The 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=210=5
7. The triangle area - from two legs
8. Calculate the heights of the right triangle from its area.
9. Calculation of the inner angles of the triangle - basic use of sine function
10. 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.11. 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.R=2c=24.4=2.2
12. 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:
- triangle
- right triangle
- Heron's formula
- The Law of Sines
- The Law of Cosines
- Pythagorean theorem
- triangle inequality
- similarity of triangles
- The right triangle altitude theorem