# Sin Rule & Pythagoras?

1. Jan 25, 2009

### MrPickle

1. The problem statement, all variables and given/known data
The two sides of a stepladder are of length 2m and 1.85m. When fully opened, the longer side is inclined at 65° to the horizontal. Find the distance apart of the feet of the step ladder.

2. Relevant equations
Sin Rule & Pythagoras?

3. The attempt at a solution
I had a go but I really think it's wrong.

$\frac{2}{\sin90°} = \frac{b}{\sin65°}$

$b = \frac{2}{\sin90°}\times \sin65°$

$b = 1.81 (2d.p.)$

$a^2 = 2^2 - 1.81^2 = 0.7239$

$a = 0.85 (2d.p.)$

$x^2 = 1.85^2 - 0.85^2 = 2.7$

$x = 1.64 (2d.p.)$

$l = 1.81 + 1.64 = 3.45m$

P.S. How do you do new lines in LaTeX?

2. Jan 25, 2009

### Bacat

Re: Ladder

How do you know that the top angle is 90 degrees when it is fully opened? I think you have to stick with just the 65 degree angle and the leg lengths in order to find the distance.

Also, I don't know how to do new lines in LateX. I always just close the tex tag and start a new one.

3. Jan 26, 2009

### MrPickle

Re: Ladder

I thought it would be 90 degrees because it says 65 degree to the horizontal.

4. Jan 26, 2009

### chaoseverlasting

Re: Ladder

You cant assume that the ladder opens up at 90 degrees (it doesnt actually).

5. Jan 26, 2009

### MrPickle

Re: Ladder

I see what I did wrong. I got horizontal and verticle mixed up so I drew my diagram wrong.

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