Question
An infinte plane is tiled with equilateral triangles of side length 9cm. If you drop a coin of radius 1 cm onto the plane, what is the probability the coin lands within one of the triangles?
Answers
R_Scott
"within" is taken to mean "not touching a side"
the center of the coin must land inside of a "nested" inner triangle
whose edges are parallel to the 9 cm triangle and .5 cm inside
the ratio of the areas of the inner and outer triangles is the probability
the center of the coin must land inside of a "nested" inner triangle
whose edges are parallel to the 9 cm triangle and .5 cm inside
the ratio of the areas of the inner and outer triangles is the probability
R_Scott
the side length of the inner triangle is ... 9 - √3
the ratio of the areas is the square of the ratio of the side lengths
the ratio of the areas is the square of the ratio of the side lengths