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# 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

Shubham Kumar Kumar 2 months, 1 week ago

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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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