We will start with the triangle ABCm with AC = 44 and BC = 32
We work out the angle BAC, labelled as x° in the diagram shown below
Using the trigonometry ratio, we have
[tex]tan(x)= \frac{opposite}{adjacent} [/tex]
[tex]tan(x)= \frac{32}{44} [/tex]
[tex]x= tan^{-1} (\frac{32}{44}) [/tex]
[tex]x=36[/tex]° (rounded to the nearest integer)
Then we work out the size of angle y°, shown in the diagram below.
By using the angles in a triangle rule, we have
y°=180°-(90°+36°)= 54°
Then we use this information to work out the length of CD
[tex]tan (y)= \frac{BC}{CD} [/tex]
[tex]tan(54)= \frac{32}{CD} [/tex]
[tex]CD= \frac{32}{tan(54)} [/tex]
[tex]CD=23[/tex] (to the nearest integer)
