Geometry Forum - Problem of the Week Solutions - Jill and Jimmy - At the Movies, April 4-8, 1994 Hilary Aleksa ____________________ Using the movie screen as the base, draw a triangle to where Joaquin thinks the best seat is. Then draw a circle so that the triangle is inscribed in the circle. The screen then becomes a chord of the circle. Therefore, the 30 degree angle intercepts the arc which corresponds with the screen (chord). Any other angle formed in the theater that intercepts that same arc is also 30 degrees. Juanita, as a result, is the correct one; there is more than one seat meeting those qualifications. Allison Sullivan ____________________ --Juanita is right, because if a circle is drawn around the picture given, so that the screen is a chord of the circle, then all the inscribed angles intercepting this chord (the screen) will equal 30 degrees. Therefore, there is more than 1 seat that will have a line of sight of 30 degrees. --Theorem: If inscribed angles intercept the same arc, then the inscribed angles are congruent. --If angles intercept the same arc, then they intercept the same chord. Therefore, all the inscribed angles that have the screen as an intercepted chord have the measure of 30 degrees. Dale Carothers ____________________ My name is Dale Carothers, and I am a student at Shaler Area School District. I am sending you my solution for the problem of the week for April 4-8. I found Juanita to be right. There are other places where the viewing angle is 30 degrees. The screen and the viewing angle form a triangle. Since a triangle has 180 degrees, and the viewing angle must be 30 degrees, the sum of the other 2 angles must equal 150 degrees. The angles can be a variety of measures equalling 150 degrees. By changing the measures of the 2 angles the location of the seat, which has a 30 viewing angle, will change. Therefore Juanita is right. Drew Ludwig ____________________ Jaunita is correct, because the seats are not in the same plane as the screen. Therefore, even if two lines are drawn at 30 degree angle and point at exactly one seat, these lines could be moved up or down to another location, and the angles would still be 30 degrees. Also, you speak of the movie screen as if it was a line, and it is not.(It is probalbly a rectangle.) How would you know where to measure the angles from? Pete DeFilippo ____________________ Juanita is right because you could sit perpendicularto the right or left side of the sreen forming a 90 degree angle with the screen leaving the other angle in the triangle to be 60 degrees. There are many other possibilities for where they can sit. Previous page || Next problem || Previous problem || Table of Contents || Forum Home Page