Problem C. 883.

Order KöMaL!

ELTE

Competitions Portal

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 points)

Deadline expired.

Sorry, the solution is published in Hungarian only.

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 $\varepsilon$ =10,89^o.

Statistics on problem C. 883.

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

Our web pages are supported by:

ELTE