Solve the Problem $$\mathrm { h } = \frac { \mathrm { d } } { \cot \mathrm { A } - \cot \mathrm { B } } \mathrm { ft } \text {. }$$

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 d ft closer is B, then the height of the object is given by $$\mathrm { h } = \frac { \mathrm { d } } { \cot \mathrm { A } - \cot \mathrm { B } } \mathrm { ft } \text {. }$$
Find $\mathrm { A }$ if $\mathrm { h } = 50 \mathrm { ft } , \mathrm { d } = 20 \mathrm { ft }$ , and $\mathrm { B } = 61 ^ { \circ }$ . Give your answer in degrees to the nearest hundredth.

A) $55.72 ^ { \circ }$
B) $39.97 ^ { \circ }$
C) $46.34 ^ { \circ }$
D) $51.51 ^ { \circ }$