Question

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.

NCERT Class X
Mathematics - Mathematics

Chapter _SOME APPLICATIONS OF
TRIGONOMETRY

Answer 1

Diagram is in attachment below
Let                       AB = h meters.
therefore,  In right ΔABC, we have:
                            AB/AC = tan θ
  ⇒                      h/9 = tan θ               .......(1)
In right ΔABD, we have:
                            AB/AD = tan (90°- θ) = cot θ
  ⇒                       h/4 = cot θ              .......(2)
  Multiplying (1) and (2), we get 
            h/9 × h/4 = tan θ ×cot θ = 1       {tan θ X cot θ =1}
  ⇒          h²/36 = 1 ⇒ h² = 36
  ⇒          h =  ± 6 m
  ⇒          h = 6 m                {height is positive only}
          Thus, the height of the tower is 6 m. 
MARK IT AS BEST

2d57c4d04f4d845c250a4b1e614a7045.docx