Chapter 4.1, Problem 86PE

A winch on a sailboat is $8\text{ in}\text{.}$ in diameter and is used to pull in the "sheets" (ropes used to control the corners of a sail). To the nearest degree, how far should the winch be turned to pull in $2\text{ ft}$ of rope?

Before the widespread introduction of electronic devices to measure distances, surveyors used a subtense bar to measure a distance $x$ that is not directly measurable. A subtense bar is a bar of known length $h$ with marks or “targets" at either end. The surveyor measures the angle $\theta$

formed by the location of the surveyor's scope and the top and bottom of the bar (this is the angle subtended by the bar). Since the angle and height of the bar are known, right triangle trigonometry can be used to find the horizontal distance. Alternatively, if the distance from the surveyor to the bar is large, then the distance can be approximated by the radius $r$ of the arc $s$ intercepted by the bar. Use this information for Exercises 87-88.