Mark:
BERMUDA TRIANGLE
sin(75)/sin(45) = 1.3660254
The answer is (1 + \/3) / 2 meters or approximately 1.36 meters
First, determine the measures of the angles using 3x + 4x + 5x = 180 degrees.
The angles measure 45, 60, and 75 degrees respectively.
(1) You can solve the problem by basic geometry if you draw an altitude from the vertex of the 75 degree angle to the opposite base (the longest side). This altitude divides the original triangle into two smaller triangles (a 45-45-90 triangle and a 30-60-90 triangle). You can now determine the measures of all the sides.
(2) An alternative method is to use the Law of Sines to set up the problem (As Mark did).
Call the length of the short side S and the length of the longest side L.
Then sin(75) / L = sin(45) / S
Since S = 1 meter, sin (75) = .9659258 and sin(45) = .7071,
It follows that L = 1.366 meters.
May I assume this problem defeated the combined knowledge of A2K?
"Mark drove to work at 40 mph and arrived 1 minute late.
The next day, he left at the same time and drove the same distance to work at 45 mph and arrived 1 minute early.
How far did Mark have to drive to work?"
Yeah!!!
TTH:
.
L
.I
LINES
.E
.S
Lines crossed
Egocentrism over posts: can we communicate as well as we think? Overestimating the obviousness of one's intentions can lead to insufficient allowances for ambiguities in communication. This philosophy may account for the fact that I don't read PM's and therefore oblivious to any clues.
"Hint:involves a bus"
"
there was no car involved
"
Clever; the drop off point for the bus was higher than the pickup point! Or, the other way round?
FODRRMEASSL
TRESJEUDCTDIENON