Question

what is \\(\sin 45^\circ\\)?

a. \\(\frac{1}{\sqrt{2}}\\)

b. \\(\frac{1}{2}\\)

c. 1

d. \\(\sqrt{2}\\)

Explanation:

Identify the given triangle properties

Using the Special Right Triangles and 45-45-90 Triangle Theorem knowledge points

$$
LATEXBLOCK0
$$

Apply the definition of the sine ratio

We define the sine of an angle in a right triangle as the ratio of the length of the opposite side to the length of the hypotenuse.

$$ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} $$

Calculate the value of sine 45 degrees

Substitute the known side lengths from our triangle into the ratio.

$$ \sin(45^\circ) = \frac{1}{\sqrt{2}} $$

Answer:

• (A) \(\frac{1}{\sqrt{2}}\) (Correct answer)
• (B) \(\frac{1}{2}\)
• (C) 1
• (D) \(\sqrt{2}\)