Thread: Law of Sines and Cosine problem help...I'm stumped.

1. Law of Sines and Cosine problem help...I'm stumped.

http://img100.imageshack.us/img100/6232/dscn1765mw2.jpg

A 125-ft tower is located on the side of a mountain that is inclined 32(degrees) to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 55; ft downhill from the base of the tower. Find the shortest length of the wire needed.

I plug some things into the law of cosines and I get to
3025 = 15625b^2 - 250b*cos(58)

For the love of god help, this is due tomorrow -_-

2. Hello, MmmmSteak!

A 125-ft tower is located on the side of a mountain that is inclined 32° to the horizontal.
A guy wire is to be attached to the top of the tower and anchored at a point 55 ft
downhill from the base of the tower.
Find the shortest length of the wire needed.
Code:
                          o A
* |
*   |
*     |125
*       |
x *    122° o B
*       *58°|
*     *       |
*   * 55        |
* * 32°           |
C o - - - - - - - - - o D

The tower is: .$\displaystyle AB = 125$
The guy wire is: .$\displaystyle x = AC$
And: .$\displaystyle BC = 55$

$\displaystyle \angle BCD = 32^o$
. . Then: .$\displaystyle \angle CBD = 58^o$
. . Hence: .$\displaystyle \angle ABC = 122^o$

Law of Cosines: .$\displaystyle x^2 \;=\;125^2 + 55^2 - 2(125)(55)\cos122^o \;=\;25936.38988$

Therefore: .$\displaystyle x \;=\;161.0477876 \;\approx\;\boxed{161\text{ ft}}$

3. I actually just finished working this out (with help of a friend) when I got your reply, and this was my answer. This is so incredibly difficult...

I have two more.

5. Write the trigonomic expression (cot[x])/(csc[x]-sin[x]) in terms of sine and cosine, and simplify.
8. Use the formulas for lowering powers to rewrite the expression cos^4[x] in terms of the first power of cosine.

I got something on #5, but it wasn't right so I scrapped it. I don't know what #8 is talking about.

Thank you so very, very much for you help.