Calculating the Value of sin(45°) in a Right Triangle Using Trigonometric Functions

sin(45°)

The sine function, denoted as sin, is a trigonometric function that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse of the triangle

The sine function, denoted as sin, is a trigonometric function that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse of the triangle. In other words, the sine of an angle is equal to the length of the side opposite that angle divided by the length of the hypotenuse.

To find sin(45°), we can use the fact that in a 45°-45°-90° right triangle, the two legs are congruent. Let’s assume the length of each leg is 1.

Therefore, in the given right triangle:
Opposite side = 1
Hypotenuse = sqrt(2) (using the Pythagorean theorem)

Now we can calculate sin(45°) by dividing the length of the opposite side by the length of the hypotenuse:
sin(45°) = opposite side / hypotenuse
= 1 / sqrt(2)
= sqrt(2) / 2

So, sin(45°) is equal to sqrt(2) / 2.

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