40 70 70 triangle

Acute isosceles triangle.

Sides: a = 40   b = 70   c = 70

Area: T = 1341.64107865
Perimeter: p = 180
Semiperimeter: s = 90

Angle ∠ A = α = 33.2033099198° = 33°12'11″ = 0.58795034029 rad
Angle ∠ B = β = 73.3988450401° = 73°23'54″ = 1.28110446254 rad
Angle ∠ C = γ = 73.3988450401° = 73°23'54″ = 1.28110446254 rad

Height: ha = 67.0822039325
Height: hb = 38.33325939
Height: hc = 38.33325939

Median: ma = 67.0822039325
Median: mb = 45
Median: mc = 45

Inradius: r = 14.907711985
Circumradius: R = 36.52224436325

Vertex coordinates: A[70; 0] B[0; 0] C[11.42985714286; 38.33325939]
Centroid: CG[27.14328571429; 12.77875313]
Coordinates of the circumscribed circle: U[35; 10.4354983895]
Coordinates of the inscribed circle: I[20; 14.907711985]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.7976900802° = 146°47'49″ = 0.58795034029 rad
∠ B' = β' = 106.6021549599° = 106°36'6″ = 1.28110446254 rad
∠ C' = γ' = 106.6021549599° = 106°36'6″ = 1.28110446254 rad

Calculate another triangle




How did we calculate this triangle?

a = 40 ; ; b = 70 ; ; c = 70 ; ;

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

p = a+b+c = 40+70+70 = 180 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 180 }{ 2 } = 90 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 90 * (90-40)(90-70)(90-70) } ; ; T = sqrt{ 1800000 } = 1341.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1341.64 }{ 40 } = 67.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1341.64 }{ 70 } = 38.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1341.64 }{ 70 } = 38.33 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 40**2-70**2-70**2 }{ 2 * 70 * 70 } ) = 33° 12'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 70**2-40**2-70**2 }{ 2 * 40 * 70 } ) = 73° 23'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 70**2-40**2-70**2 }{ 2 * 70 * 40 } ) = 73° 23'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1341.64 }{ 90 } = 14.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 40 }{ 2 * sin 33° 12'11" } = 36.52 ; ;




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

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