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wu :: forums    riddles    putnam exam (pure math) (Moderators: william wu, Eigenray, SMQ, towr, Icarus, Grimbal)    A High School level Problem (Interesting) « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: A High School level Problem (Interesting)  (Read 8376 times) daemonturk Newbie     Posts: 46 A High School level Problem (Interesting)   « on: Jul 27th, 2009, 3:47am » Quote Modify A straight track on a hillside makes an angle of 50 degrees with the line of greatest slope and an angle of 11 degree 28 minutes with the horizontal. Find the angle the hillside makes with the horizontal.     Cookies goes to the shortest and simplest solution.   « Last Edit: Jul 27th, 2009, 3:47am by daemonturk » IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: A High School level Problem (Interesting)   « Reply #1 on: Jul 27th, 2009, 4:24am » Quote Modify Are the 50° measured horizontally (as on a map) or in 3D? IP Logged daemonturk Newbie     Posts: 46 Re: A High School level Problem (Interesting)   « Reply #2 on: Jul 27th, 2009, 8:51am » Quote Modify For that particular angle, 3D. IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: A High School level Problem (Interesting)   « Reply #3 on: Jul 27th, 2009, 9:13am » Quote Modify 18°? IP Logged daemonturk Newbie     Posts: 46 Re: A High School level Problem (Interesting)   « Reply #4 on: Jul 27th, 2009, 9:21am » Quote Modify Correct. But working? IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: A High School level Problem (Interesting)   « Reply #5 on: Jul 27th, 2009, 9:35am » Quote Modify Let's call alpha = 11°28, beta = 50°, and gamma the hill slope.   If we take a unit length l of track and call h is the altitude difference, then     h = l·sin(alfa)   On the other side, if d is the distance along the greatest slope that has the same difference, we have     d = l·cos(beta) and     h = d·sin(gamma)   All this together gives     sin(gamma) = h/d = sin(alfa)/cos(beta).   It would be clearer with a picture that shows where the right angles are. « Last Edit: Jul 27th, 2009, 9:36am by Grimbal » IP Logged daemonturk Newbie     Posts: 46 Re: A High School level Problem (Interesting)   « Reply #6 on: Sep 1st, 2009, 4:21am » Quote Modify Ya. IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs => putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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