Solve the Problem $\mathrm { d } \mathrm { ft }$

Multiple Choice

Solve the problem.
-It can be shown that if the angle of elevation from an observer to the top of an object is A and the angle of elevation $\mathrm { d } \mathrm { ft }$ closer is $\mathrm { B }$ , then the distance from the object to the closest point of observation is given by
$$\mathrm { D } = \frac { \mathrm { d } \cot \mathrm { B } } { \cot \mathrm { A } - \cot \mathrm { B } } \mathrm { ft } \text {. }$$
Find $B$ if $D = 20 \mathrm { ft } , \mathrm { d } = 30 \mathrm { ft }$ , and $A = 51 ^ { \circ }$ . Give your answer in degrees to the nearest hundredth.

A) $51.00 ^ { \circ }$
B) $64.09 ^ { \circ }$
C) $72.05 ^ { \circ }$
D) $61.64 ^ { \circ }$