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.

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 is opposite to the measure of ∠O and the length required is the adjacent side to the m∠O. According to the trigonometric relations:

Substituing:

Using a calculator, tan(5) = 0.0875:

The length of to the nearest tenth of a foot is 53.68 feet.