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

question 28

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) \(61.64 ^ { \circ }\)

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