Final answer:
The sine of the smallest interior angle of a right triangle with legs 8 and 6 inches is found by using the Pythagorean theorem to first calculate the hypotenuse, which is 10 inches, and then taking the ratio of the opposite side (6 inches) over the hypotenuse, resulting in 0.6.
Step-by-step explanation:
The question asks for the sine of the smallest interior angle in a right triangle with legs 8 and 6 inches respectively. First, we should identify which leg is opposite the smallest angle. In a right triangle, the smallest interior angle is opposite the shortest leg. In this case, the smallest angle is opposite the 6-inch leg.
To find the sine of the smallest angle, we need to know the length of the hypotenuse. Using the Pythagorean theorem, which states that for a right triangle with legs a and b and hypotenuse c, the relationship between these sides is a² + b² = c². By plugging in our known leg lengths, we get 8² + 6² = c², which simplifies to 64 + 36 = c², or 100 = c². Hence the hypotenuse c is √100, which is 10 inches.
Now, 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. Thus, the sine of the smallest interior angle, which is opposite the 6-inch side, is 6/10. This simplifies to 0.6 or 3/5.