If the hypotenuse of a right triangle measures 10 units and the length of the opposite side is 6 units, what is the value of the cosecant of the angle opposite the 6-unit side?

To find the value of the cosecant of the angle opposite the 6-unit side, we first note that cosecant is the reciprocal of the sine function. The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the sine of the angle (let's call it θ) can be calculated as follows: \[ \sin(θ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{6}{10} = 0.6 \] Now, the cosecant of the angle would be the reciprocal of the sine: \[ \csc(θ) = \frac{1}{\sin(θ)} = \frac{1}{0.6} \approx 1.6667 \] So, the value of the cosecant of the angle opposite the 6-unit side is approximately 1.67.