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Mathematics · Some Applications of Trigonometry · NCERT Examples

Example 3

A complete, independently verified solution for NCERT Example 3.

Mathematics · Chapter 9 · NCERT Examples

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Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.

NCERT Example

Example 3

observer height · chimney

An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. Find the height of the chimney.

Observer CD viewing the top A of chimney AB at an angle of elevation of 45 degrees.
Figure 9-6 from the supplied NCERT chapter.

Solution

Board-exam working:

Let AE be the part of the chimney above the observer's eye level.

DE=CB=28.5 mDE=CB=28.5\text{ m}
tan⁡45∘=AEDE\tan45^\circ=\frac{AE}{DE}
1=AE28.51=\frac{AE}{28.5}
AE=28.5 mAE=28.5\text{ m}
AB=AE+EB=28.5+1.5=30 mAB=AE+EB=28.5+1.5=30\text{ m}

Final answer

The chimney is 30 m high.