NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 8: Introduction to Trignometry and Its Applications - Exercise 8.1

Question 1

Step 1: Recall the definition of cosine in a right triangle.

\(\cos A = \dfrac{\text{Base}}{\text{Hypotenuse}}\)

Here, \(\cos A = \dfrac{4}{5}\).

This means Base = 4 units, Hypotenuse = 5 units.

Step 2: Find the third side (Perpendicular) using Pythagoras theorem.

\( \text{Hypotenuse}^2 = \text{Base}^2 + \text{Perpendicular}^2 \)

\( 5^2 = 4^2 + \text{Perpendicular}^2 \)

\( 25 = 16 + \text{Perpendicular}^2 \)

\( \text{Perpendicular}^2 = 25 - 16 = 9 \)

\( \text{Perpendicular} = 3 \)

Step 3: Recall the definition of tangent.

\( \tan A = \dfrac{\text{Perpendicular}}{\text{Base}} \)

\( \tan A = \dfrac{3}{4} \)

Final Answer: \(\dfrac{3}{4}\) (Option B).