In ΔOPQ, the measure of ∠Q=90°, the measure of ∠O=5°, and PQ = 4.6 feet. Find the length of QO to the nearest tenth of a foot.

Answers

Answer 1

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.

In OPQ, The Measure Of Q=90, The Measure Of O=5, And PQ = 4.6 Feet. Find The Length Of QO To The Nearest

Answer 2

Answer:

52.6

Explanation:

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