Question

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.

Answer 1

52.6

Step-by-step explanation:

Answer 2

Answer:
`\overline{QO} =` 53.68 ft

Step-by-step 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
`\overline{PQ}` is opposite to the measure of ∠O and the length required is the adjacent side to the m∠O. According to the trigonometric relations:

`tan\theta=(opp)/(adj)`

Substituing:

`tan(5)=\frac{4.6}{\overline{QO}}`

Using a calculator, tan(5) = 0.0875:

`\overline{QO}=(4.6)/(0.0875)`

`\overline{QO}=53.68`

The length of
`\overline{QO}` to the nearest tenth of a foot is 53.68 feet.