Question 1035430: A set of wooden planks is to be arranged in an equilateral triangle shape in a circular pool, with the points of the triangle touching the edge of the pool. What is the total length of the planks needed if the pool has a radius of 5 meters?
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi there,
If you connect the radius from
each of the points of the triangle
to the center of the pool bisecting
the 60 degree angles , you form
3 isosceles triangles.
The angle at the center is 120 degrees
with 30 degrees at the two equal angles.
Using A,B and C to denote the points of
one of the isosceles triangles, you have:-
Cos A = 120 degrees.
AB = 5 m
AC = 5 m
BC^2 = AB^2 + AC^2 - 2(AB) x (AC) x Cos(A)
BC^2 = 5^2 + 5^2 - 2(5) x (5)x cos(120)
BC^2 = 75
BC = π75
BC = 8.7 meters
3 x 8.7 = 26.1 meters
The total length of planks required.
Hope this helps :-)
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