Isosceles triangle calculator (B,b) - the result
Obtuse isosceles Triangle.
The lengths of the sides of the triangle:a = 24
b = 24
c = 42.38114844572
Area: T = 238.76328208959
Perimeter: p = 90.38114844572
Semiperimeter: s = 45.19107422286
Angle ∠ A = α = 28° = 0.48986921906 rad
Angle ∠ B = β = 28° = 0.48986921906 rad
Angle ∠ C = γ = 124° = 2.16442082725 rad
Altitude to side a: ha = 19.89769017413
Altitude to side b: hb = 19.89769017413
Altitude to side c: hc = 11.26773175069
Median: ma = 32.28114979888
Median: mb = 32.28114979888
Median: mc = 11.26773175069
Inradius: r = 5.28334454386
Circumradius: R = 25.56106536183
Vertex coordinates: A[42.38114844572; 0] B[0; 0] C[21.19107422286; 11.26773175069]
Centroid: CG[21.19107422286; 3.75657725023]
Coordinates of the circumscribed circle: U[21.19107422286; -14.29333361114]
Coordinates of the inscribed circle: I[21.19107422286; 5.28334454386]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 152° = 2.6532900463 rad
∠ B' = β' = 152° = 2.6532900463 rad
∠ C' = γ' = 56° = 0.97773843811 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: Side b and Angle β
b=24 β=28°
2. From the Side b, we calculate Side a:
a=b=24
3. From the Angle β, we calculate Angle α:
α=β α=28°
4. From the Angle α and Side a, we calculate Altitude hc:
sinα=h:a h=a⋅ sinα=24⋅ sin(28°)=11.267
5. From the Side a and altitude h, we calculate side c - Pythagorean theorem:
a2=(c/2)2+h2 c=2 a2−h2=2⋅ 242−11.2672=42.381
6. From the Side a and side c, we calculate Perimeter p:
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).
7. The triangle perimeter is the sum of the lengths of its three sides
8. 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.9. Calculate the height of the isosceles triangle.
10. The triangle area
11. Calculation of the inner angles of the triangle - symmetry
12. 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.13. 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.14. 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.Solve Another Triangle
