Question

Consider right triangle APQR below.P2.9RWhich expressions represent the length of side PR?Choose 2 answers:Otan(80° -20°)O tan (90° -20°)1tan(20)1tan(100° -20°)

Answer 1

Given the triangle below:

To find the length of side PR, we use trigonometric ratio.

Where

`\begin{gathered} PQ\Rightarrow opposite \\ QR\Rightarrow hypotenuse \\ PR\Rightarrow adjacent \end{gathered}`

From trigonometric ratio,

`\begin{gathered} \tan\theta=(opposite)/(adjacent) \\ where \\ \theta=20\degree \\ thus, \\ \tan20=(PQ)/(PR) \\ thus, \\ PR=(PQ)/(\tan20) \end{gathered}`

Given that PQ = 1, we have

`PR=(1)/(\tan20)`

Recall from trigonometric identities:

`\begin{gathered} (1)/(\tan\theta)=cot\text{ }\theta \\ cot\text{ }\theta\text{ =}\tan(90-\theta) \end{gathered}`

Thus, we have

`PR\text{ = }(1)/(\tan20)=\tan(90-20)`

Hence, the expressions that represent the length of side PR are

`\begin{gathered} \tan(90\degree-20\degree) \\ (1)/(\tan(20\degree)) \end{gathered}`

The correct options are B and C