Answer
$ x=10\tan\theta\sin\theta$
Work Step by Step
Let c be the shared side.
In the upper triagle (with given side 10),
the third angle is $ 90^{o}-\theta$,
c is the leg opposite to $\theta,$ so
$\displaystyle \tan\theta=\frac{c}{10}\ \Rightarrow\ c=10\tan\theta$
In the lower triangle (with side x),
the lower left acute angle is complementary with the ($ 90^{o}-\theta$) angle, so it is equal to $\theta,$
x is the leg opposite to $\theta,$
c is the hypotenuse, so
$\displaystyle \sin\theta=\frac{x}{c} \ \Rightarrow\ x=c\sin\theta=10\tan\theta\sin\theta$
$ x=10\tan\theta\sin\theta$
