[F3] MATHS 問題

(1) Given three points A(1,2) , B(5,-6) and C(11,k) , if AB // BC , find the value of k.
if AB // BC , then the slope of AB =the slope of BC
[2-(-6)/1-5]=(-6-k)/(5-11)
-2=(-6-k)/-6
-6-k=12
k=-18
(2)The gradient of a path is 1:12. Find the inclination of the path, corret to 1 decimal place.[Show your working]
Let the inclination of the path be θ
tanθ=1/12

θ~4.8o (corret to 1 decimal place)

(3)The bearings fo A and B from O are N50o W and N40o E respectively.Given that OB=1 km and AB=2km, find the bearing if B from A
Notice that ∠AOB=(40o +50o )=90o
sin∠OAB=1/2
∠OAB=30o
the bearing from A to B is S(30+50)o E=S80o E