Question

Determine whether each expression can be used to find the length of side RS.

Answer 1

`\begin{gathered} \sin (R)\rightarrow\text{ Yes} \\ \tan (T)\rightarrow\text{ No} \\ \cos (R)\rightarrow\text{ No} \\ tan(R)\rightarrow\text{ No} \end{gathered}`

Explanation:

Since we know a side and the hypotenuse, we can rule out tangent and cotangent, since these are related to the two legs.

Therefore, if we want to know that side we must apply sine or cosine, just like this:

`\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{ hypotenuse}} \\ \text{therefore, in this case:} \\ \sin R=(21)/(35) \\ \cos \theta=\frac{\text{adjacent}}{\text{ hypotenuse}} \\ \cos R=\frac{\text{unknown}}{35} \end{gathered}`

Therefore, the way to calculate the value of the missing side is by means of the sine of the angle R