ExamBro
ExamBro
TS EAMCET · Maths · Heights and Distances

A tower, of \(x\) metres high, has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant \(y\) metres from the foot of the tower. Then, the length of the flagstaff (in metres), is

  1. A \(\frac{y\left(x^2-y^2\right)}{\left(x^2+y^2\right)}\)
  2. B \(\frac{x\left(y^2+x^2\right)}{\left(y^2-x^2\right)}\)
  3. C \(\frac{x\left(x^2+y^2\right)}{\left(x^2-y^2\right)}\)
  4. D \(\frac{x\left(x^2-y^2\right)}{\left(x^2+y^2\right)}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{x\left(y^2+x^2\right)}{\left(y^2-x^2\right)}\)

Step-by-step Solution

Detailed explanation

Let \(B C\) be the height of tower and \(C D\) be height of the flagstaff, Let \(C D=h\) Since, the tower and flagstaff makes equal angle, i.e. \(\theta\) In \(\triangle B A C\), \(\tan \theta=\frac{x}{y}\) ...(i) In \(\triangle D A B\),…