What is the gage block height for an angle of 9 degrees on a 10-inch sine plate?

• A. 1.5543 inches
• B. 1.4643 inches
• C. 1.6643 inches
• D. 1.5643 inches

Answer: (D)

To determine the correct gage block height for an angle of 9 degrees on a 10-inch sine plate, we need to utilize the sine function, which relates the height of the gage block to the sine of the angle and the length of the sine plate.

The formula used in this context is:

Height = Length × sin(Angle)

When the angle is 9 degrees and the length of the sine plate is 10 inches, we can first convert the angle from degrees to radians, or directly use the sine function in degrees:

Height = 10 inches × sin(9 degrees)

Calculating this gives us the height requirement for the gage block to achieve the desired angle. Using a scientific calculator, we find that sin(9 degrees) is approximately 0.1564.

Thus,

Height ≈ 10 inches × 0.1564 ≈ 1.5643 inches.

This calculation shows that the gage block height for an angle of 9 degrees on a 10-inch sine plate is indeed 1.5643 inches, making this the correct answer. This precise measurement is essential for ensuring accurate angular setups and workpiece positioning when using a sine plate in machining or inspection activities.