Question

sin 45° answer 1 \\(sqrt{3}\\) \\(\frac{sqrt{2}}{2}\\) \\(\frac{1}{2}\\)

Explanation:

Step1: Recall 45-45-90 triangle ratios

In a right isosceles triangle, legs are equal, hypotenuse = $a\sqrt{2}$ (where $a$ = leg length).

Step2: Apply sine definition

$\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$. For $\theta=45^\circ$, $\sin45^\circ = \frac{a}{a\sqrt{2}} = \frac{\sqrt{2}}{2}$ (rationalized form).

Answer:

$\frac{\sqrt{2}}{2}$