Multiple choice

An electrician has to repair an electric fault on a pole of height $5$m. She needs to reach a point $1.3$m below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at an angle of $60^0$ to the horizontal, would enable her to reach the required position? Also, how far the foot of the pole should she place the foot of the ladder? ( You may take $\sqrt3=1.73$).

  1. $\text{length of ladder}=7.4m$ , $\text{distance}=2.14m$
  2. $\text{length of ladder}=4.27m$ , $\text{distance}=3.7m$
  3. $\text{length of ladder}=4.27m$ , $\text{distance}=2.14m$
  4. $\text{length of ladder}=4.7m$ , $\text{distance}=2.14m$
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C Correct answer
Explanation

Height to reach = 5 - 1.3 = 3.7m. Ladder length L = 3.7 / sin(60) = 3.7 / (sqrt(3)/2) = 7.4 / 1.73 = 4.277m. Distance from pole = 3.7 / tan(60) = 3.7 / 1.73 = 2.138m.

AI explanation

The total vertical height the electrician needs to reach is 5 m minus 1.3 m, which equals 3.7 m. The ladder forms a right-angled triangle with the pole and the ground, where the height is 3.7 m and the angle with the ground is 60 degrees. Using the sine formula, the length of the ladder is 3.7 / sin(60 degrees), which equals 3.7 / (1.732 / 2), resulting in a length of approximately 4.27 m. To find the distance of the foot of the ladder from the pole, we use the tangent formula: distance = 3.7 / tan(60 degrees), which is 3.7 / 1.732, equaling approximately 2.14 m.

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