Question

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.

Answer 1

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.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer:

6

Step-by-step explanation:

tan x = h/4

tan(90-x) = cotx= h/9

1 = h^2 /36

h = √36 = 6