5 15 15 triangle

Acute isosceles triangle.

Sides: a = 5   b = 15   c = 15

Area: T = 36.97554986444
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 19.18881364537° = 19°11'17″ = 0.33548961584 rad
Angle ∠ B = β = 80.40659317731° = 80°24'21″ = 1.40333482476 rad
Angle ∠ C = γ = 80.40659317731° = 80°24'21″ = 1.40333482476 rad

Height: ha = 14.79901994577
Height: hb = 4.93300664859
Height: hc = 4.93300664859

Median: ma = 14.79901994577
Median: mb = 8.29215619759
Median: mc = 8.29215619759

Inradius: r = 2.11328856368
Circumradius: R = 7.60663882926

Vertex coordinates: A[15; 0] B[0; 0] C[0.83333333333; 4.93300664859]
Centroid: CG[5.27877777778; 1.64333554953]
Coordinates of the circumscribed circle: U[7.5; 1.26877313821]
Coordinates of the inscribed circle: I[2.5; 2.11328856368]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.8121863546° = 160°48'43″ = 0.33548961584 rad
∠ B' = β' = 99.59440682269° = 99°35'39″ = 1.40333482476 rad
∠ C' = γ' = 99.59440682269° = 99°35'39″ = 1.40333482476 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 5 ; ; b = 15 ; ; c = 15 ; ;

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

p = a+b+c = 5+15+15 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-5)(17.5-15)(17.5-15) } ; ; T = sqrt{ 1367.19 } = 36.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.98 }{ 5 } = 14.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.98 }{ 15 } = 4.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.98 }{ 15 } = 4.93 ; ;

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{ 15**2+15**2-5**2 }{ 2 * 15 * 15 } ) = 19° 11'17" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5**2+15**2-15**2 }{ 2 * 5 * 15 } ) = 80° 24'21" ; ; gamma = 180° - alpha - beta = 180° - 19° 11'17" - 80° 24'21" = 80° 24'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.98 }{ 17.5 } = 2.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5 }{ 2 * sin 19° 11'17" } = 7.61 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 15**2 - 5**2 } }{ 2 } = 14.79 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 5**2 - 15**2 } }{ 2 } = 8.292 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 5**2 - 15**2 } }{ 2 } = 8.292 ; ;
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