Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem C. 883. (January 2007)

C. 883. A trough with regular triangular cross section is filled to the brim with water. Through what angle should it be tilted in order to make one fifth of the water flow over? The triangular ends of the trough should move in their vertical planes.

(5 pont)

Deadline expired on February 15, 2007.


Sorry, the solution is available only in Hungarian. Google translation

Megoldás: Tekintsük a vályú keresztmetszetét megdöntött állapotban.

Ekkor a szinusz-tétel szerint \frac{x}{a}=\frac{\sin\varepsilon}{\sin60^{\circ}} és \frac{4x}{a}=\frac{\sin(60^{\circ}-\varepsilon)}{\sin60^{\circ}}. A két egyenletet egymással elosztva (nem 0-val osztunk):

4=\frac{\sin(60^{\circ}-\varepsilon)}{\sin\varepsilon},

amiből kifejtés majd átrendezés után \tg\varepsilon=\frac{\sqrt3}{9}, és így \varepsilon=10,89o.


Statistics:

295 students sent a solution.
5 points:224 students.
4 points:21 students.
3 points:11 students.
2 points:11 students.
0 point:26 students.
Unfair, not evaluated:2 solutions.

Problems in Mathematics of KöMaL, January 2007