wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Question 16
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.


Open in App
Solution

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=ABBC
tan x=AB4
AB=4 tan x...(i)
Also,
In right ΔABD,
tan (90x)=ABBD
cot x=AB9
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.

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon