why do we need a protractor in measuring traffic cone?

Answer 1

It's like answer 1 said, except the ratio of the slant height to the radius of the bottom is 1/cosine, not the tangent, of the angle between the bottom of the cone and its side. It is also equal to 1/sine of half the angle of the cone at its apex. So the easiest way to do this is to divide the radius by the slant height, find the angle whose sine equals the result, and double that to get the cone angle.

Answer 2

Actually, you don't. I assume that you wish to measure the angle between two opposite elements of a cone; you can do this by placing a protractor on one side at the tip of the cone and placing a ruler against the other side, and reading the protractor where the ruler crosses it. But, if you don't have a protractor, you can measure the angle this way: measure the slant height of the cone with a tape measure. Turn it on its side and measure the diameter of the bottom; divide by 2 to get the radius. Divide the slant height by the radius. Use a scientific calculator or book of tables to find the angle whose tangent equals the result of the division; this gives the angle between the bottom of the cone and its side. Subtract this from 90 degrees to get the angle between a side and a vertical line, and double this to get the angle between the two sides.