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Mathematics · Some Applications of Trigonometry · NCERT Examples

Example 2

A complete, independently verified solution for NCERT Example 2.

Mathematics · Chapter 9 · NCERT Examples

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NCERT Example

Example 2

ladder · angle of elevation

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. What length of ladder, inclined at 60° to the horizontal, is required? How far from the foot of the pole should the ladder be placed? Take √3 = 1.73.

A ladder BC leaning against pole AD to reach point B, making a 60 degree angle with the ground.
Figure 9-5 from the supplied NCERT chapter.

Solution

Board-exam working:

The height reached on the pole is:

BD=5−1.3=3.7 mBD=5-1.3=3.7\text{ m}

Let BC be the ladder.

sin⁡60∘=BDBC\sin60^\circ=\frac{BD}{BC}
32=3.7BC\frac{\sqrt3}{2}=\frac{3.7}{BC}
BC=3.7×23=7.41.73≈4.28 mBC=\frac{3.7\times2}{\sqrt3}=\frac{7.4}{1.73}\approx4.28\text{ m}

Let DC be the distance of the ladder from the pole.

tan⁡60∘=BDDC\tan60^\circ=\frac{BD}{DC}
3=3.7DC\sqrt3=\frac{3.7}{DC}
DC=3.71.73≈2.14 mDC=\frac{3.7}{1.73}\approx2.14\text{ m}

Final answer

Required ladder length ≈ 4.28 m; distance from the pole ≈ 2.14 m.