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Some Applications Of Trigonometry

Question
CBSEENMA10009789
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On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower.

Solution

                       

Let AB be the tower with height h.

Let x be the angle of elevation from c.

So, the angle of elevation from D is (90-x).

           ..........( Since the angle of elevation from C and D are complementary)

In ∆CAB,tan x = ABAC⇒tanx = h4      .........(i)In ∆DAB,tan(90-x) = ABAD⇒tan(90-x) = h16⇒cot x = 16h    ...........(ii)From (i) and (ii) ,tan x  ×  cot x = h4 x h16⇒1 = h264⇒h2 = 64⇒h = 64⇒h = 8 mHence, the height of the tower is 8 m.

Some More Questions From Some Applications of Trigonometry Chapter

Choose the correct option and justify your choice:
sin 2A = 2 sin A is true when A = 
(A) 0°         (B) 30°         (C) 45°       (D) 60°

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