A man standing on the top of a hill and sees a flagpole he knows is 45 feet high. The angle of depression to the bottom of the p
ole is 12 degrees, and the angle of elevation to the top of the pole is 16 degrees. Find his distance from the pole
1 answer:
Answer:
<h3>160.44 feet</h3>Explanation:
check the attachment for the diagram of the set up for proper clarification.
From the diagram, the man's distance from the pole is labelled AB.
To get AB =, we need to get side CB first which is equal to ED i.e ED = CB.
From ΔCDE, opposite side = 45 feet and the adjacent is ED.
USing TOA, according to trig function SOH, CAH, TOA;
tan 16° = opp/adj = BD/ED
tan 16° = 45/ED
ED = 45/tan 16°
ED = 156.93 feet
Since ED = CB, hence CB = 156.93 feet
From ΔABC, adj = CB and hypotenuse = AB. According to CAH;
cos 12° = adj/hyp = CB/AB
cos 12° = 156.93/AB
AB = 156.93/cos 12°
AB = 160.44 feet
<em>Hence the man's distance from the pole is 160.44 fe</em>et
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