Solution:
Given the triangle below:
To find the length of side PR, we use trigonometric ratio.
Where
[tex]\begin{gathered} PQ\Rightarrow opposite \\ QR\Rightarrow hypotenuse \\ PR\Rightarrow adjacent \end{gathered}[/tex]
From trigonometric ratio,
[tex]\begin{gathered} \tan\theta=\frac{opposite}{adjacent} \\ where \\ \theta=20\degree \\ thus, \\ \tan20=\frac{PQ}{PR} \\ thus, \\ PR=\frac{PQ}{\tan20} \end{gathered}[/tex]
Given that PQ = 1, we have
[tex]PR=\frac{1}{\tan20}[/tex]
Recall from trigonometric identities:
[tex]\begin{gathered} \frac{1}{\tan\theta}=cot\text{ }\theta \\ cot\text{ }\theta\text{ =}\tan(90-\theta) \end{gathered}[/tex]
Thus, we have
[tex]PR\text{ = }\frac{1}{\tan20}=\tan(90-20)[/tex]
Hence, the expressions that represent the length of side PR are
[tex]\begin{gathered} \tan(90\degree-20\degree) \\ \frac{1}{\tan(20\degree)} \end{gathered}[/tex]
The correct options are B and C
