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Applications of Trigonometry
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17/06/2021 12:04 pm
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The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.
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17/06/2021 12:06 pm
Let AB be the tower. C and D be the two points with distance 4 m and 9 m from the base respectively.
In right ΔABC,
tan x = AB/BC
tan x = AB/4
AB = 4 tan x … (i)
Again, from right ΔABD,
tan (90°-x) = AB/BD
cot x = AB/9
AB = 9 cot x … (ii)
Multiplying equation (i) and (ii)
AB2 = 9 cot x × 4 tan x
⇒ AB2 = 36 (because cot x = 1/tan x
⇒ AB = ± 6
Since height cannot be negative. Therefore, the height of the tower is 6 m.