Determine the value of x
Starting by adding some lengths like it is shown in the next figure
Determine the value of $x$
Starting by adding some lengths like it is shown in the next figure
We assume $\overline{RQ}=d$, and $\overline{QS}=b$.
hence, we have $tan(20)^{0}=\frac{RQ}{PS}$
$tan(50)^{0}=\frac{RQ}{QS}=\frac{d}{b}$
$\implies d=bsin(50^{0})=atan(20^{0})$
$\implies \frac{a}{b}=\frac{tan(50^{0})}{tan(20^{0})}$
From the next $\triangle PKS$,
$tan (10^{0})=\frac{c}{a}$
Also, from $\triangle QKS$
$tan x=\frac{c}{b}$
$\implies \frac{a}{b}= \frac{tan(x)}{tan(10^{0})}$
Using the two results above,
$\frac{tan(x)}{tan(10^{0})}=\frac{tan(50^{0})}{tan(20^{0})}$
$\implies tan(x)=\frac{tan(50^{0})}{tan(20^{0})}(tan(10^{0}))$
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