Q13 of 47 Page 1

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.



Let AB be the tower and B be the foot,


Given, C and D are at distances of 4 m and 16 m from foot,


⇒ BC = 4 m


⇒ BD = 16 m


Also, angles of elevation from C and D to top A are complementary.


⇒ ∠ACB + ∠ADB = 90°


Let ∠ACB = θ


⇒ θ + ∠ADB = 90°


⇒ ∠ADB = 90° - θ


Now, in ∆ABC




[1]


In ∆ABD




[From 1]


⇒ AB2= 64


⇒ AB = 8 m


Height of tower is 8 meter.


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