In a right triangle, when dealing with an angle [tex]\(\theta\)[/tex], we often refer to three primary trigonometric ratios: sine, cosine, and tangent. The sine of an angle [tex]\(\theta\)[/tex] is defined as the ratio of the length of the opposite side to the length of the hypotenuse.
Let's go through the steps to find the sine of [tex]\(\theta\)[/tex]:
1. Identify the Opposite Side and Hypotenuse:
- The opposite side to the angle [tex]\(\theta\)[/tex] is given as 3 units.
- The hypotenuse of the triangle is given as 5 units.
2. Apply the Definition of Sine:
- The sine of an angle [tex]\(\theta\)[/tex] is calculated using the formula:
[tex]\[
\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}
\][/tex]
3. Substitute the Given Values:
- Substitute the length of the opposite side (3 units) and the length of the hypotenuse (5 units) into the formula:
[tex]\[
\sin(\theta) = \frac{3}{5}
\][/tex]
4. Perform the Division:
- Calculate the division of 3 by 5:
[tex]\[
\frac{3}{5} = 0.6
\][/tex]
Thus, the sine of the angle [tex]\(\theta\)[/tex] is [tex]\(0.6\)[/tex].
