A couple of questions...

[Coffee]

Hi guys,

Having a few problems with the questions I've attached below. The answer to question 5 is 244m, 7a is 44.6, and 7b is 36 but I'm getting completely different answers and I'm not sure where I'm going wrong. If someone could provide an explanation/working out that would be great!

[MightyBeh]

First one:

Spoiler

First step, set up a diagram of the information you have. Here's mine:

(note that the 10km is on the horizontal because the information was from a map, which is flat. Bit of an awkward question)
So first, we know that we need the value of y to do very much with this triangle. Thankfully, this is pretty easy to work out:

We don't have the value of the hypotenuse to use Pythagoras', so we'll have to use some trig to find x.



There's two ways to do this question with these. Sine's out because the hypotenuse is irrelevant to the question; so that leaves cosine or tan. Whichever one you use is up to you - I'll show both.

using cosine

In this case it's more correct to have your answer in metres, so the answer is 244 metres.

using tan

We can swap x and tan, like so:

Same thing as with cosine - answer in metres. (244m)

Second one:

Spoiler

Pretty much the same thing for part a, one of the trig functions to find x.


= 44.6m

Second one's a bit different - we have to use an inverse to find the angle.




Also worth mentioning that your book seems kind of inconsistent on how far you should round - I actually think that 7b should be 37.

That should be it, let me know if it's not clear

[Coffee]

Ah, you're a gem! Thanks so much

Also yeah, I've noticed the textbook is a little odd when it comes to rounding. Just wondering so I know for next year, would I be deducted marks on the end of year exam if my answer is a point or so off? Like with 7a the answer is 44.6 but my calculator gives me 44.5, would the assessors care if I wrote 44.5 instead of 44.6?

[BakedDwarf]

Ah, you're a gem! Thanks so much

Also yeah, I've noticed the textbook is a little odd when it comes to rounding. Just wondering so I know for next year, would I be deducted marks on the end of year exam if my answer is a point or so off? Like with 7a the answer is 44.6 but my calculator gives me 44.5, would the assessors care if I wrote 44.5 instead of 44.6?

Straight from the assessment reports:

Rounding off should only occur at the final answer stage in a question, not halfway through the calculation. However, in cases where the answer to a previous question must be used, the rounded version of the previous answer may be used without penalty. (Students could also use the unrounded version of the previous answer without penalty.)

So, really, it depends upon the question.

[MightyBeh]

Ah, you're a gem! Thanks so much

Also yeah, I've noticed the textbook is a little odd when it comes to rounding. Just wondering so I know for next year, would I be deducted marks on the end of year exam if my answer is a point or so off? Like with 7a the answer is 44.6 but my calculator gives me 44.5, would the assessors care if I wrote 44.5 instead of 44.6?

You're welcome! What calculator do you use? That seems a bit odd.
Like Dwarf said, you're probably fine though.

[Coffee]

Thanks to both of you

You're welcome! What calculator do you use? That seems a bit odd.
Like Dwarf said, you're probably fine though.

And I use the TI-Nspire CX CAS.