NCERT · Class 10 · Mathematics · Introduction to TrigonometryIf $\tan \theta = \frac{4}{3}$, then the value of $\sin \theta$ is:
Step-by-Step Solution
We know that $\tan \theta = \frac{\text{Perpendicular}}{\text{Base}} = \frac{4}{3}$. Using Pythagoras theorem, Hypotenuse = $\sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$. Therefore, $\sin \theta = \frac{\text{Perpendicular}}{\text{Hypotenuse}} = \frac{4}{5}$.
Detailed Options Breakdown
Option : 3/5
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.
Option 1: 4/5 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: 3/4
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.
Option 3: 5/4
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.
💡 Study Guide: This question tests core syllabus concepts from Introduction to Trigonometry. For formulas, key summaries, and mock exam reference guides, read the full Introduction to Trigonometry Revision Notes.