A/P/V Question

Question

It's late… too late. You should have been home an hour ago and the door is locked. Luckily, you left your bedroom window unlocked, knowing that a ladder was in the backyard.
The bottom of your window is 25 m from the ground and the ladder is 30 m long. Unfortunately, the neighbours' unfriendly pit bull is chained to a pole that is 26 m from your house with a chain that is 10 m long.

A) Draw and fully label a diagram for the situation described above.
B) What is the distance from the base of the ladder to your house (to the nearest tenth of a metre)?
C) How far is the ladder from the pole?
D) Will you be able to get into your room without the dog getting you first? Justify your answer fully.

Answer 1

A)  Diagram

          |\

          |   \ 30m

          |     \

25m   |        \

         |          \ 

         |___x___\dog

            16m       *-----------| pole

                                10m

 

25m for height from ground to window

30m for length of ladder

16m from house to dog's closest reach (26m-10m chain = 16m)

x = distance from house to base of ladder

 

B)  For Pythagorean theorem we need to find x

 

25² + x² = 30²

x² = 900-625

x = √275

x ≅ 16.6m

the base of the ladder is 16.6m out from the house.

 

 

C) The ladder is 16.6m from the house

     The pole is 26m from the house

     The ladder is 26-16.6 = 9.4m from the pole

 

D) The dog will be able to reach you as you try to mount
the ladder because the dog can come within 16m of
the house and the base of the ladder is 16.6m out from the

house.  There is a 0.6m area of overlap.