NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 8: Introduction to Trignometry and Its Applications - Exercise 8.3

Question 10

Step 1: Draw the situation in your mind.

• The ladder is \(15\,\text{m}\) long. This is the hypotenuse of a right triangle.
• The wall is vertical, so the height of the wall will be the vertical side of the triangle.
• The ladder makes an angle of \(60^\circ\) with the wall.

Step 2: Identify which trigonometric ratio to use.

• We know the hypotenuse (ladder length = \(15\,\text{m}\)).
• We want to find the side adjacent to the angle with the wall (the vertical height).
• So we use the cosine function: \(\cos\theta = \dfrac{\text{adjacent}}{\text{hypotenuse}}\).

Step 3: Apply the formula.

\[ \cos 60^\circ = \dfrac{\text{Height of wall}}{15} \]

Step 4: Substitute the value of \(\cos 60^\circ\).

\[ \dfrac{1}{2} = \dfrac{\text{Height of wall}}{15} \]

Step 5: Solve for the height.

\[ \text{Height of wall} = 15 \times \dfrac{1}{2} = 7.5 \]

Step 6: Write the final answer with unit (SI).

\[ \text{Height of wall} = 7.5\,\text{m} \]