NCERT Class X Chapter 9: Some Application Of Trigonometry Example 3

NCERT Class X Chapter 9: Some Applications of Trigonometry Example 3

Question:

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°. What is the height of the chimney?

Given:

  • Height of observer = \(1.5\,\text{m}\)
  • Distance from observer to chimney = \(28.5\,\text{m}\)
  • Angle of elevation = \(45^\circ\)

To Find:

Height of the chimney

Formula:

\[ \tan \theta = \frac{\text{Opposite side}}{\text{Adjacent side}} \]

Solution:

Step 1: Let the height of the chimney above the observer's eyes be \( h \) meters.

Step 2: Using the right triangle formed, apply the tangent formula:

$$ \tan 45^\circ = \frac{h}{28.5} $$

Step 3: Since \( \tan 45^\circ = 1 \), substitute and solve for \( h \):

$$ 1 = \frac{h}{28.5} \implies h = 28.5 $$

Step 4: Total height of the chimney is the sum of \( h \) and the observer's height.

$$ \text{Total height} = h + 1.5 = 28.5 + 1.5 = 30\,\text{m} $$

Result:

The height of the chimney is \(30\,\text{m}\).

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