The angles of elevation of the …
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The angles of elevation of the top of a tower from two points at a distance of 4m 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
Posted by _Jass_ Mahey_ 2 months, 1 week ago
- 2 answers
Muhammad Amaan Rahman 𝔸𝕄𝔸𝔸ℕ 𝕄𝕌ℍ𝔸𝕄𝕄𝔸𝔻 2 months, 1 week ago
Let AB be the height of tower and x be the one of the complementry angle.
So, (90-x) be the another complementary angle.
C and D be the two points with distance 4 m and 9 m from the base respectively.
As per question,
In right ΔABC, ⇒tan x=AB/BC
⇒tan x=AB/4
⇒AB=4 tan x...(i)
Also,
In 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
⇒AB= ±6
Height cannot be negative.
Therefore, the height of the tower is 6m.
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Shubham Kumar Kumar 2 months, 1 week ago
1Thank You