a. What is the length of the longest pole that can be carried horizontally aroun

Question

a. What is the length of the longest pole that can be carried horizontally around a corner at which a 3-ft corridor and a 4-ft corridor meet at right angles? b. what is the length of the longest pole that can be carried horizontally around a corner at which a corridor that is a ft wide and a corridor that is b ft wide meet at right angles? c. what is the length of the longest pole that can be carried horizontally around a corner at which a corridor that is a=5 ft wide and a corridor that is b= 5ft wide meet at an angle of 120 degrees? d. What is the length of the longest pole that can be carried around a corner at which a corridor that is a ft wide and a corridor that is b ft wide meet at right angles, assuming there is an 8-ft ceiling and that you may tilt the pole at any angle?

Explanation / Answer

a) 5 ft using pythagoras theorem b) sqrt( a^2 + b^2) c) pole length = 2.5*sqrt(3) because in the triangle formed at the corner, drawing a right triangle with 5ft as one of the sides and the angle opposite to it is 60 degrees hence sin(60) = 5/ pole lenght d) the longest pole would be the diagonal treating the intersection to be a cuboid hence the longest pole length would be sqrt( a^2 + b^2 + 64)

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