Answer: [tex]\overline{QO} =[/tex] 53.68 ft
Explanation: Since ∠Q is 90°, ΔOPQ is a right triangle. So, there are hypotenuse, opposite side and adjacent side. And there the trigonometric relations: sine, cosine and tangent.
The image of the triangle is below.
Side [tex]\overline{PQ}[/tex] is opposite to the measure of ∠O and the length required is the adjacent side to the m∠O. According to the trigonometric relations:
[tex]tan\theta=\frac{opp}{adj}[/tex]
Substituing:
[tex]tan(5)=\frac{4.6}{\overline{QO}}[/tex]
Using a calculator, tan(5) = 0.0875:
[tex]\overline{QO}=\frac{4.6}{0.0875}[/tex]
[tex]\overline{QO}=53.68[/tex]
The length of [tex]\overline{QO}[/tex] to the nearest tenth of a foot is 53.68 feet.
