# working out 'x' which is a side of a scalene inside a right-angle

• Apr 10th 2008, 09:21 AM
Jamie88
working out 'x' which is a side of a scalene inside a right-angle
http://users.cs.cf.ac.uk/J.G.Lee/triangle
Hello everybody.

I was just wondering how one would calculate the length of x on the diagram above. The questions after this in my work are easier so I think I must be missing something easy here as well.

it's not tan 50 100/x is it...?

Any help would be brill, thank you. :)
• Apr 10th 2008, 09:26 AM
Moo
Hello,

If we name from up to down the points on the right side : A (summit), B, C, D (summit of right angle), what is x ? ;-)
• Apr 10th 2008, 09:45 AM
Jamie88
That's confused me... :s
• Apr 10th 2008, 05:31 PM
Soroban
Hello, Jamie!

[quote]
Code:

    A o       * *     x *50°*       *    *       *      *     D o        *       *  *      *       *      *  10°*       *          *  *       *          30°  * *     C o * * * * * * * * * o B               100

In right triangle $DCB\!:\;\;\tan30^o \:=\:\frac{CD}{100}\quad\Rightarrow\quad CD \:=\:100\tan30^o\;\;{\color{blue}[1]}$

In right triangle $ACB\!:\;\;\tan40^o \:=\:\frac{AC}{100}\quad\Rightarrow\quad AC \:=\:100\tan40^o\;\;{\color{blue}[2]}$

But $AC \:=\:x + CD\quad\Rightarrow\quad x \:=\:AC - CD\;\;{\color{blue}[3]}$

Substitute [1] and [2] into [3]: . $\boxed{x \;=\;100\tan40^o - 100\tan30^o}$

• Apr 13th 2008, 07:29 AM
Jamie88
Brilliant, thank you for your help. :)