Marissa has a wool rug that has the shape of a regular octagon in her living room. The diameter of the incircle of the rug measu
res 7 feet approximately. Which of the following is the approximate measure of one of the sides of wool rug? A.2.9 feet
B. 3.5 fest
C. 3.7 feet
D. 4.1 feet
I did it a different way. One including trigonometry. The question only tells the apothem, "diameter of the incircle." Apothem is the line segment from the center to the midpoint of segments in regular polygons. Incircle is a circle that connects all the midpoints in a regular polygon. You are trying to find the side. The angle of view is from the central angle, which is 45 degrees in an octagon. We have to split 45 in half, because when you try to find distance in a line segment, you do it through trig and trig requires a right triangle. Since you are finding the side, you need tangent. The angle of view (I don't know if that's the actual name), it touches the apothem, which would be adjacent. The line that the angle isn't touching is the opposite. And tanganent uses both of those. The formula I used is tan(22.5)/1 = o/7. These are fractions. Then you cross multiply the fractions, so tan(22.5) goes with 7 and o goes with 1. When you cross multiply, you pretty much multiply the opposite fraction's side. The formula then would be o = tan(22.5) x 7. And that equals 2.9.
