Multiple choice

A straight highway leads to the foot of a tower of height 50 m. From the top of the tower, angles of depressions of two cars standing on the highway are $\displaystyle 30^{\circ}$ and $\displaystyle 60^{\circ}$. what is the distance between the cars. ?

  1. $43.3 m$
  2. $57.73 m$
  3. $86.6 m$
  4. $100 m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the tower height be h = 50. The distance of the first car is 50/tan(60) = 50/sqrt(3) and the second is 50/tan(30) = 50*sqrt(3). The distance between them is 50*(sqrt(3) - 1/sqrt(3)) = 50*(2/sqrt(3)) = 100/1.732 = 57.73 m.

AI explanation

Using the trigonometric ratios for angles of depression, the distance of the farther car is 50 divided by tan(30), which equals 50 times sqrt(3). The distance of the closer car is 50 divided by tan(60), which equals 50 divided by sqrt(3). Subtracting the closer distance from the farther distance gives 50 times sqrt(3) minus 50 divided by sqrt(3), which equals 100 divided by sqrt(3), or approximately 57.73 m.

Keep practicing — related questions