Final answer:
To find the horizontal side of a right triangle with a given angle, use the cosine function multiplied by the length of the hypotenuse. Since the angle in radians is unspecified, we cannot provide a numerical answer without this critical information.
Step-by-step explanation:
Calculating the Length of the Horizontal Side in a Right Triangle
To find the length of the horizontal side of a right triangle when an angle is given, we can use trigonometric functions. First, let's clarify that by "horizontal side" the question might be referring either to the adjacent side (if the given angle is between the horizontal side and the hypotenuse) or to the opposite side (if the angle is between this side and the hypotenuse). However, since the angle measurement is not provided in the question, we'll assume a standard naming where the horizontal side is the adjacent side to the angle in question.
Assuming we have an angle (let's call it \( \theta \)) and want to find the length of the adjacent side (\( x \)), we can use the cosine function which is defined as:
\[ \cos(\theta) = \frac{\text{Adjacent side}}{\text{Hypotenuse}} \]
Rearranging for the length of the adjacent side, we get:
\[ x = \cos(\theta) \times \text{Hypotenuse} \]
Since the hypotenuse is given as 6 inches, we would substitute that value into the equation. However, without the precise angle measurement in radians, we cannot give a numerical answer. If the angle was provided (for example, \( \frac{\pi}{4} \) radians), we would calculate:
\[ x = \cos\left(\frac{\pi}{4}\right) \times 6 \]
We would then use a calculator to find the cosine of \( \frac{\pi}{4} \) radians and multiply that by 6 to get the length of the horizontal side.
For the purpose of a generalized approach, if the actual angle in radians was given, such as \( \pi \) radians (which does not apply in this case as \( \pi \) radians is 180 degrees and cannot be an angle in a right triangle), the calculation steps would still be applicable with the correct numeric angle.