Multiple choice

A student sitting in a classroom sees a picture on the black board at a height of $1.5$m from the horizontal level of sight. The angle of elevation of the picture is $30^{\circ} $. As the picture is not clear to him, he moves straight towards the black board and sees the picture at an angle of elevation of $45^{\circ} $. Find the distance by which the student moves.

  1. $1.098$m
  2. $2.098$m
  3. $3.098$m

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let h = 1.5m. Distance d1 = h / tan(30) = 1.5 * sqrt(3) approx 2.598m. Distance d2 = h / tan(45) = 1.5 * 1 = 1.5m. The distance moved is d1 - d2 = 2.598 - 1.5 = 1.098m.

AI explanation

Let the initial distance be x and the final distance be y. Using the basic trigonometric ratio for tangents, tan 30 = 1.5 divided by x and tan 45 = 1.5 divided by y. This yields x = 1.5 times the square root of 3 and y = 1.5. The distance moved is x minus y, which is 1.5 times 1.732 minus 1.5, resulting in 1.098 m.

Keep practicing — related questions