Desperate little sister

[beezy4eva]

Hey guys, my little sister has her maths exam tomorrow (not VCE, year 10) and is desperate for some help with this question. Since all knowledge of maths has vacated my mind, I was hoping someone could give me a hand:
[IMG]http://img819.imageshack.us/img819/8524/flagpoleq.png[/img]

Uploaded with ImageShack.us
The question is find the height of the flagpole
Sorry about the crappy image
I also think something may be missing. But I've copied the question exactly how it appears in the book, so maybe I've just gotten stupid(er)

[/0]

I think we need another angle.. or some other information

[beezy4eva]

Thanks for verifying that. I did get the feeling it seemed a bit hard for year 10 trig. I think the angle next to the 15 is missing, as in the book there's a line pointing to it, but nothing written. I just wanted to double check though, its been a while since I've done trig...

[Russ]

You can find the height of the flagpole but not the height of the flag itself

[funkyducky]

Use trigonometry - tan(15degrees)=height/120
(SOHCAHTOA ring any bells?)

[HERculina]

angle is definitely missing since its height of the flagpole your looking for. maybe youre actually meant to measure the angle with a protractor?

[funkyducky]

Wait, they want the height including the flag? Something is definitely missing.

[onerealsmartass]

yeah there's an angle missing...

[pi]

yeah there's an angle missing...

Definitely, not possible otherwise

[chrisjb]

There is technicaly a way to solve it... but based on the way these questions are usualy worded, you can assume the book left an angle out.

first of all, we'll call the right angled triangle with 15 degrees Triangle A, and the other iregular (almost triangle) shape with the very acute angle which we must find Triangle B.

The fact that we know two of the angles in Triangle A means we can easily find the third. This third side is 75 degrees. From this, if you draw an imaginary line from the top of Triangle A, directly up (like an extension of the farthest left side of Triangle A) you can then work out one angle of Triangle B (which is now actualy a triangle).

- it doesn't matter that you have changed one in that triangle by drawing this line because the third (farthest right) angle is the only one that matters.

From that, you can find that one angle in Triangle B is 105 degrees. This is because the obtuse angle in Triangle B and the previously unknown side in triangle A- which we discovered to equal 45 degrees must add up to 180 (cos they are on a straight line). Then, we can find (using the cosine rule on Triangle A) one side of Triangle B (the bottom side) is ~124.23 meters.

I know that using variations of the sine, cosine and tan rule which work on non right angled triangles you can then find the important angle (the verry acute one next to the 15 degrees), but it is too late at night for me to do that now. I'll edit this post later with explanatory pics and finish off the equation, but I am sure that it is possible to finish it, only the final step remains.

EDIT: My bad... you can only find the height of the flag if the flag were to be positioned on the farthest right hand side of the rectangle it's on. Technicaly the people didn't leave out an angle, they left out a side length of that stupid rectangle.

I'll still finish as much of the problem as I can tomorrow (I feel like doing some maths )