Calculating the Distance between the Feet of a Stepladder: Sin Rule & Pythagoras

[MrPickle]

Homework Statement

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.

Homework Equations

Sin Rule & Pythagoras?

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?

 

[Bacat]

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.

 

[MrPickle]

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

 

[chaoseverlasting]

You can't assume that the ladder opens up at 90 degrees (it doesn't actually).

 

[MrPickle]

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