VCAA 2009 Geo and Trig exam 1, question 9

[claire92]

I'm having serious issues with this question, and I really am not making sense of why it would be C (2.3m) and what formula is best to use.

Sorry if this has been done to death, but I really can't seem to nut it out.

*I've attached the question to this post

[onerealsmartass]

hey,
first thing to do is use cosine rule to find the angle M. Then use SOHCAHTOA to find the lenght of the point T to the wall.
Once this is done you can find the angle that T makes with the wall using SOHCAHTOA, then pythagoras to find the height

[lorcan_raven]

Firstly imagine the pole falls and hits the centre of the wall so it's tilting.
Therefore now imagine the TRIANGLE that is made by the pole (4) the bottom of the pole and the corner of the wall (also 4) and the new length from centre of wall to the corner (x). using pythagora's theorem, x is found.

Now, with x found, imagine the OTHER triangle that is made from x, the corner of the wall to the point on the ground BELOW the pole's tip, and then the verticle from the ground to the tip of the pole. You assume that this length along the ground is half of the full length, because it is the highest point that this pole could lean, and so it is 3. Then with 3, and x, you again you pythagora's to find the final length (the height) which is the answer.

Sorry I didn't do the actual working I find it hard to work algebra on the computer haha.

[lorcan_raven]

Actually disregard what I just said, it was wrong. Onerealsmartass was correct.
Find the angle M, with cosine rule, then use that and the two lengths other side in a Pythagorean theorem to find the length between the wall and the pole. Then it's just THAT new length, and the pole (hypotenuse) to find the height.
Sorry!

[claire92]

Thanks guys, I'm still not getting the correct answer, so I think I might just go monday morning for the formula from my teacher.

Im thinking this might be the 'distinguishing' question for the geo nd trig module.

[VCE123456789]

 A =COS^-1 (6^2 + 4^2 - 5^2 ) = 56 degrees

sin 56 = x/4
x= 3.31

h= square root of 4^2 - 3.31^2

and hence h= 2.3 (which is C)

Do u get it know?  

[menashiiii]

haahaha i just did this
and sat there for a good 10 minutes thinking
whadda faarrr?!

[onerealsmartass]

haha yeah my friend at school was like duuuuuudddeee... WTF is with this question?? my teacher cant even answer it so do you reckon you can? other friend: of course he can!
i sorta knew i had to use pythagoras to get the height, but took me like 5 minutes of thinking to actually get it... lol what a killer question in an exam, pretty harsh

[menashiiii]

deffs adding it to my book!

[onerealsmartass]

yeah for sure was quite difficult, i woudltn be surprised if there was antoher relatively challenging question to finish off trig otherwise it should be pretty straightforward.
more worried about matrices SA to be honest everyone is talking it up to be 'hard'... i hope not

[claire92]

Thanks VCE123456789! I do get it now, makes it alot clearer.

Will be adding this to my cheatbook!

[coolwhip]

defs adding to the summary book

thanks smartass.