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Posted by alana_96 (U15249580) on Tuesday, 1st May 2012
Hi, I'm stuck on question 3 and question 5 on the 2003 calculator paper. I've tried various methods to try and solve both of them, but I still keep getting the wrong answers! The questions are:
Q3. 2 yachts leave from harbour H. Yacht A sails on a bearing of 072 degrees for 30km and stops. Yacht B sails on a bearing of 140 degrees for 50km and stops. How far apart are the two yachts when they have both stopped? DO NOT USE A SCALE DRAWING.
Q5. The number of diagonals, d, in a polygon with n sides is given by the formula- d= n(n-3)/2.
A polygon has 20 diagonals. How many sides does it have?
I would really appreciate it if someone could point me in the right direction!
Posted by Maths Teacher BBC (U15178780) on Wednesday, 2nd May 2012
3) - Cosine Rule: Use angle 140° - 72° = 68°
Now the angle is 68° and the two sides are 30 and 50.
This will work out correctly.
5) - Substitue the 20 in:
20 = n(n - 3)/2
20 x 2 = n(n - 3)
40 = n² - 3n
n² - 3n - 40 = 0
(n - 8)(n + 3) = 0
n = 8 and n = -3
n = 8 as you can't be a negative length