SOLUTION: A circular clock has dots on its boundary which indicate the numbers 1 to 12. The dots representing 10 and 2 are 24cm apart. Find the radius of the clock.

Algebra ->  Triangles -> SOLUTION: A circular clock has dots on its boundary which indicate the numbers 1 to 12. The dots representing 10 and 2 are 24cm apart. Find the radius of the clock.      Log On


   

Question 1102459: A circular clock has dots on its boundary which indicate the numbers 1 to 12. The dots representing 10 and 2 are 24cm apart. Find the radius of the clock.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
The angle formed by the hands would be 120 degrees
So the other angles of the would be 30 degrees each in the isosceles triangle
so we now have one side 24 cm and the three angles
so we can use ASA
Uses law of sines to determine unknown sides then Heron's formula and trigonometric functions to calculate area and other properties of given triangle.

Obtuse isosceles triangle.
Sides: a = 13.856   b = 13.856   c = 24
Area: T = 83.138
Perimeter: p = 51.713
Semiperimeter: s = 25.856
Angle ∠ A = α = 30° = 0.524 rad
Angle ∠ B = β = 30° = 0.524 rad
Angle ∠ C = γ = 120° = 2.094 rad
Height: ha = 12
Height: hb = 12
Height: hc = 6.928
Median: ma = 18.33
Median: mb = 18.33
Median: mc = 6.928
Inradius: r = 3.215
Circumradius: R = 13.856
Vertex coordinates: A[24; 0] B[0; 0] C[12; 6.928]
Centroid: CG[12; 2.309]
Coordinates of the circumcenter: U[12; -6.928]
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AAS
Obtuse isosceles triangle.
Sides: a = 24   b = 13.856   c = 13.856
Area: T = 83.138
Perimeter: p = 51.713
Semiperimeter: s = 25.856
Angle ∠ A = α = 120° = 2.094 rad
Angle ∠ B = β = 30° = 0.524 rad
Angle ∠ C = γ = 30° = 0.524 rad
Height: ha = 6.928
Height: hb = 12
Height: hc = 12
Median: ma = 6.928
Median: mb = 18.33
Median: mc = 18.33
Inradius: r = 3.215
Circumradius: R = 13.856
Vertex coordinates: A[13.856; 0] B[0; 0] C[20.785; 12]
Centroid: CG[11.547; 4]
Coordinates of the circumcenter: U[6.928; 12]