To answer this question, we can use one of the trigonometric ratios since we have a right triangle here. We also need to know that the reference angle is Having this information into account, we can use the following trigonometric ratio:
[tex]\tan (\theta)=\frac{opp}{adj}[/tex]That is, we have the value of the opposite side, and we will have the value for tan(5). Then, we have:
[tex]\tan (5)=\frac{QP}{QO}=\frac{4.6}{QO}[/tex]Now, we have to solve the equation for QO:
1. Multiply each side of the equation by QO:
[tex]QO\cdot\tan (5)=\frac{4.6}{QO}\cdot QO\Rightarrow QO\cdot\tan (5)=4.6[/tex]2. Divide both sides of the equation by tan(5):
[tex]QO\cdot\frac{\tan(5)}{\tan(5)}=\frac{4.6}{\tan(5)}\Rightarrow QO=\frac{4.6}{\tan (5)}[/tex]Therefore, we have that QO is:
[tex]QO=\frac{4.6ft}{0.0874886635259}\Rightarrow QO=52.5782405927ft[/tex]If we rounded this value to the nearest tenth, we have that QO = 52.6 ft.
