NCERT Class X Chapter 9: Some Application Of Trigonometry Example 1

NCERT Class X Chapter 9: Some Applications of Trigonometry Example 1

Question:

A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower.

Given:

  • Distance from the point to the foot of the tower = 15 m
  • Angle of elevation of the top of the tower = 60°

To Find:

Height of the tower

Formula:

For a right-angled triangle,

$$ \tan \theta = \frac{\text{Opposite side}}{\text{Adjacent side}} $$

Solution:

Step 1: Let the height of the tower be \( h \) metres. The distance from the point to the foot of the tower is 15 m. We form a right-angled triangle where:

  • Opposite side = height of tower = \( h \)
  • Adjacent side = distance from point to foot = 15 m
  • Angle of elevation = 60°

Step 2: Write the trigonometric ratio for tan 60°.

$$ \tan 60^\circ = \frac{h}{15} $$

Step 3: Substitute the value of \( \tan 60^\circ \).

$$ \sqrt{3} = \frac{h}{15} $$

Step 4: Solve for \( h \).

$$ h = 15 \times \sqrt{3} $$ $$ h = 15\sqrt{3} \ \text{m} $$

Result:

The height of the tower is $$15\sqrt{3} \ \text{m}$$.

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