Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 4   b = 8   c = 8

Area: T = 15.49219333848
Perimeter: p = 20
Semiperimeter: s = 10

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 75.52224878141° = 75°31'21″ = 1.31881160717 rad
Angle ∠ C = γ = 75.52224878141° = 75°31'21″ = 1.31881160717 rad

Height: ha = 7.74659666924
Height: hb = 3.87329833462
Height: hc = 3.87329833462

Median: ma = 7.74659666924
Median: mb = 4.89989794856
Median: mc = 4.89989794856

Inradius: r = 1.54991933385
Circumradius: R = 4.1311182236

Vertex coordinates: A[8; 0] B[0; 0] C[1; 3.87329833462]
Centroid: CG[3; 1.29109944487]
Coordinates of the circumscribed circle: U[4; 1.0332795559]
Coordinates of the inscribed circle: I[2; 1.54991933385]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 104.4787512186° = 104°28'39″ = 1.31881160717 rad
∠ C' = γ' = 104.4787512186° = 104°28'39″ = 1.31881160717 rad

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How did we calculate this triangle?

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

p = a+b+c = 4+8+8 = 20 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20 }{ 2 } = 10 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10 * (10-4)(10-8)(10-8) } ; ; T = sqrt{ 240 } = 15.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 15.49 }{ 4 } = 7.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 15.49 }{ 8 } = 3.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 15.49 }{ 8 } = 3.87 ; ;

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{ 8**2+8**2-4**2 }{ 2 * 8 * 8 } ) = 28° 57'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4**2+8**2-8**2 }{ 2 * 4 * 8 } ) = 75° 31'21" ; ; gamma = 180° - alpha - beta = 180° - 28° 57'18" - 75° 31'21" = 75° 31'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 15.49 }{ 10 } = 1.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4 }{ 2 * sin 28° 57'18" } = 4.13 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 8**2 - 4**2 } }{ 2 } = 7.746 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 4**2 - 8**2 } }{ 2 } = 4.899 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 4**2 - 8**2 } }{ 2 } = 4.899 ; ;
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