Question

you give tours on the great lakes and talk about points of interest. a lighthouse typically has 2 beacons that rotate together—but not necessarily facing opposite directions. in that way, it can be a shorter time between the first and second flashes than between the second flash and the third flash (when the first beacon comes around for the second time). one way of identifying which lighthouse you are looking at is to find the ratio of the short time between flashes to the long time between flashes. if the beacons are set 120° apart along the rotation, as shown below, what is this ratio? beacon 1 120° rotation beacon 2 light source top view 1:120 120:1 1:3 3:1 1:2

Explanation:

Step1: Calculate the short - time angle

The short - time between flashes corresponds to the smaller arc between the two beacons. Given that the beacons are \(120^{\circ}\) apart.

Step2: Calculate the long - time angle

The total rotation of a circle is \(360^{\circ}\). The long - time between flashes corresponds to the larger arc. The measure of the larger arc is \(360^{\circ}- 120^{\circ}=240^{\circ}\)

Step3: Find the ratio

The ratio of the short - time (angle) to the long - time (angle) is \(\frac{120^{\circ}}{240^{\circ}}=\frac{1}{2}\)

Answer:

\(1:2\)