100 141 100 triangle

Acute isosceles triangle.

Sides: a = 100   b = 141   c = 100

Area: T = 4999.911149297
Perimeter: p = 341
Semiperimeter: s = 170.5

Angle ∠ A = α = 45.17704559498° = 45°10'14″ = 0.7888373181 rad
Angle ∠ B = β = 89.65990881004° = 89°39'33″ = 1.56548462917 rad
Angle ∠ C = γ = 45.17704559498° = 45°10'14″ = 0.7888373181 rad

Height: ha = 99.99882298593
Height: hb = 70.92107303967
Height: hc = 99.99882298593

Median: ma = 111.537698938
Median: mb = 70.92107303967
Median: mc = 111.537698938

Inradius: r = 29.32549940936
Circumradius: R = 70.50112479713

Vertex coordinates: A[100; 0] B[0; 0] C[0.595; 99.99882298593]
Centroid: CG[33.53216666667; 33.33327432864]
Coordinates of the circumscribed circle: U[50; 49.70333798197]
Coordinates of the inscribed circle: I[29.5; 29.32549940936]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.832954405° = 134°49'46″ = 0.7888373181 rad
∠ B' = β' = 90.34109118996° = 90°20'27″ = 1.56548462917 rad
∠ C' = γ' = 134.832954405° = 134°49'46″ = 0.7888373181 rad

Calculate another triangle




How did we calculate this triangle?

a = 100 ; ; b = 141 ; ; c = 100 ; ;

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

p = a+b+c = 100+141+100 = 341 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 341 }{ 2 } = 170.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 170.5 * (170.5-100)(170.5-141)(170.5-100) } ; ; T = sqrt{ 24999114.94 } = 4999.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4999.91 }{ 100 } = 100 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4999.91 }{ 141 } = 70.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4999.91 }{ 100 } = 100 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 141**2+100**2-100**2 }{ 2 * 141 * 100 } ) = 45° 10'14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 100**2+100**2-141**2 }{ 2 * 100 * 100 } ) = 89° 39'33" ; ; gamma = 180° - alpha - beta = 180° - 45° 10'14" - 89° 39'33" = 45° 10'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4999.91 }{ 170.5 } = 29.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 100 }{ 2 * sin 45° 10'14" } = 70.5 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 141**2+2 * 100**2 - 100**2 } }{ 2 } = 111.537 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 100**2 - 141**2 } }{ 2 } = 70.921 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 141**2+2 * 100**2 - 100**2 } }{ 2 } = 111.537 ; ;
Calculate another triangle

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

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