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

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

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.

2. 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 ? ;-)

3. That's confused me... :s

4. 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]: . $\boxed{x \;=\;100\tan40^o - 100\tan30^o}$

5. Brilliant, thank you for your help.