35 42 35 triangle

Acute isosceles triangle.

Sides: a = 35   b = 42   c = 35

Area: T = 588
Perimeter: p = 112
Semiperimeter: s = 56

Angle ∠ A = α = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ B = β = 73.74397952917° = 73°44'23″ = 1.28770022176 rad
Angle ∠ C = γ = 53.13301023542° = 53°7'48″ = 0.9277295218 rad

Height: ha = 33.6
Height: hb = 28
Height: hc = 33.6

Median: ma = 34.47110023063
Median: mb = 28
Median: mc = 34.47110023063

Inradius: r = 10.5
Circumradius: R = 21.875

Vertex coordinates: A[35; 0] B[0; 0] C[9.8; 33.6]
Centroid: CG[14.93333333333; 11.2]
Coordinates of the circumscribed circle: U[17.5; 13.125]
Coordinates of the inscribed circle: I[14; 10.5]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ B' = β' = 106.2660204708° = 106°15'37″ = 1.28770022176 rad
∠ C' = γ' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad

Calculate another triangle


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 = 35 ; ; b = 42 ; ; c = 35 ; ;

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

p = a+b+c = 35+42+35 = 112 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 112 }{ 2 } = 56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 56 * (56-35)(56-42)(56-35) } ; ; T = sqrt{ 345744 } = 588 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 588 }{ 35 } = 33.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 588 }{ 42 } = 28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 588 }{ 35 } = 33.6 ; ;

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{ 42**2+35**2-35**2 }{ 2 * 42 * 35 } ) = 53° 7'48" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 35**2+35**2-42**2 }{ 2 * 35 * 35 } ) = 73° 44'23" ; ;
 gamma = 180° - alpha - beta = 180° - 53° 7'48" - 73° 44'23" = 53° 7'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 588 }{ 56 } = 10.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 35 }{ 2 * sin 53° 7'48" } = 21.88 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 42**2+2 * 35**2 - 35**2 } }{ 2 } = 34.471 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 35**2+2 * 35**2 - 42**2 } }{ 2 } = 28 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 42**2+2 * 35**2 - 35**2 } }{ 2 } = 34.471 ; ;
Calculate another triangle


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

See more information about triangles or more details on solving triangles.