From a 200-foot observation tower on the beach, a man sights a whale in difficulty. The angle of depression of the whale is . How far is the whale from the shoreline?
Solution: The angle of depression from the man to the whale is the angle that an imaginary line connecting the man and the whale makes with respect to the horizontal; since the man has to look downwards to spot the whale, this is called the angle of depression (if, on the other hand, he was spotting a plane in the air, he would have to look upwards and the angle would be called the elevation angle). The correct picture showing all the data is shown in Figure 1. From the right triangle, we see that , or ft (to 2 decimal places).
Figure 1 |
Observe that one may also use the complementary angle of to obtain the relation , and hence that ft, as before.
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Luis Valdez-Sanchez