Solve each problem. (Modeling) Distance between Two Points Refer to...

Solve each problem.

(Modeling) Distance between Two Points Refer to Example 3. A variation of the subtense bar method that surveyors use to determine larger distances d between two points P and Q is shown in the figure. In this case the subtense bar with length b is placed between the points P and Q so that the bar is centered on and perpendicular to the line of sight connecting P and Q. The angles a and b are measured from points P and Q, respectively. (Source: Mueller, I. and K. Ramsayer, Introduction to Surveying, Frederick Ungar Publishing Co.)

(a) Find a formula for d involving α , β , and b.

(b) Use your formula to determine d if , and b = 2.000 cm.

(Reference Example 3)

The subtense bar method is a method that surveyors use to determine a small distance d between two points P and Q. The subtense bar with length b is centered at Q and situated perpendicular to the line of sight between P and Q. See Figure 29. Angle θ is measured, and then the distance d can be determined.

(a) Find d when and b = 2.0000 cm.

(b) How much change would there be in the value of d if θ measured 1'' larger?