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

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 α and β 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 α = , and b = 2.000 cm.