Multiple choice

The height of a tower is h and the angle of elevation of the top of the tower is $\displaystyle \alpha $ on moving a distance h/2 towards the tower, the angle of elevation becomes. $\displaystyle \beta $. What is the value of$\quad \cot { \alpha } -\cot { \beta } \quad $

  1. $\displaystyle \dfrac{1}{2}$
  2. $\displaystyle \dfrac{2}{3}$
  3. $1$
  4. $2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

From the geometry, cot(alpha) = d/h and cot(beta) = (d - h/2)/h. Subtracting these gives cot(alpha) - cot(beta) = d/h - (d/h - 1/2) = 1/2.

AI explanation

Using the trigonometric ratio for cotangent, the initial distance from the observation point to the base is h times cot(alpha). After moving closer, the new distance is h times cot(beta). The difference between these distances equals h divided by 2, giving the equation h times cot(alpha) minus h times cot(beta) equals h divided by 2. Dividing the entire equation by h results in cot(alpha) minus cot(beta) equals 1/2.

Keep practicing — related questions