If 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 in the same straight line with it are complementary, find the height of the tower.
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6
Answer :
The height of the tower is 6 m.
Step-by-step explanation:
GIVEN : B and D be the two points with distance DC = 4 m and BC = 9 m from the base.
Let AC be the Height of the tower (h) and ∠CDA = θ , ∠DBA = 90° - θ (angles are complementary).
In right angle ΔACD,
tan θ = P/B = AC/CD
tan θ = h/4 ………..(1)
In right angle ΔABC,
tan (90°- θ ) = P/B = AC/BC
cot θ = h/9
1/tanθ = h/9
[cotθ = 1/tanθ ]
1/(h/4) = h/9
[from eq 1]
4/h = h/9
h² = 9 × 4
h² = 36
h = √36
h = ±6
Height can't be negative.
Hence, the height of the tower is 6 m.
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Answered by
4
Answer:
6
Step-by-step explanation:
tan x = h/4
tan(90-x) = cotx= h/9
1 = h^2 /36
h = √36 = 6
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