Multiple choice

A child is initially standing at a point on the ground, observing the top of a building, which has a height of 50 metres. The angle of elevation from the child's position to the top of the building is 30°. After walking a certain distance, denoted as d, towards the building, the angle of elevation increases by 15° from the original angle. Determine the distance (d) in cm the child walked towards the building.

  1. 360

  2. 366

  3. 3,660

  4. 36,600
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial distance x = 50 / tan(30) = 50 * sqrt(3). Final distance y = 50 / tan(45) = 50. Distance walked d = x - y = 50(sqrt(3) - 1) = 50(1.732 - 1) = 50 * 0.732 = 36.6 meters. Convert to cm: 36.6 * 100 = 3660 cm.

AI explanation

The initial distance from the building is found using tan 30 degrees equals 50 divided by the initial distance, yielding an initial distance of 50 times the square root of 3 metres. The new angle of elevation is 45 degrees, so the new distance is found using tan 45 degrees equals 50 divided by the new distance, which gives a new distance of 50 metres. The distance walked is the difference, which is 50 times the square root of 3 minus 50, or 50 times 0.732, equal to 36.6 m. Converting this distance to centimetres gives 3660 cm.

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