Question : If $\tan A=\frac{4}{3}, 0 \leq A \leq 90^{\circ}$, then find the value of $\sin A$.
Option 1: $\frac{3}{5}$
Option 2: $1$
Option 3: $\frac{3}{4}$
Option 4: $\frac{4}{5}$
Correct Answer: $\frac{4}{5}$
Solution :
Given that $\tan A = \frac{4}{3}$,
Consider a right-angled triangle where the opposite side (perpendicular) is 4 units and the adjacent side (base) is 3 units.
Using the Pythagorean theorem, the hypotenuse of this triangle can be calculated as $\sqrt{4^2 + 3^2} = 5$ units.
Therefore, $\sin A = \frac{\text{Perpendicular}}{\text{Hypotenuse}} = \frac{4}{5}$.
Hence, the correct answer is $\frac{4}{5}$.
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