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

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

• A. 1.2345 inches
• B. 1.5643 inches
• C. 1.8901 inches
• D. 1.0000 inches

Answer: (B)

To find the gage block height for a sine plate, the sine of the given angle is used in relation to the length of the sine plate. The formula for calculating the height (H) of the gage block based on the angle (A) and the length of the sine plate (L) is as follows: \[ H = L \times \sin(A) \] In this case, the length of the sine plate is 10 inches, and the angle is 9 degrees. First, the sine of 9 degrees must be calculated, which is approximately 0.1564. Then, multiplying this sine value by the length of the sine plate gives: \[ H = 10 \times \sin(9^\circ) \] \[ H = 10 \times 0.1564 \] \[ H = 1.564 \text{ inches} \] This calculation confirms the gage block height as approximately 1.5643 inches, making it the correct answer. The other options do not match this computed value for the gage block height at the given angle and sine plate length.

To find the gage block height for a sine plate, the sine of the given angle is used in relation to the length of the sine plate. The formula for calculating the height (H) of the gage block based on the angle (A) and the length of the sine plate (L) is as follows:

[ H = L \times \sin(A) ]

In this case, the length of the sine plate is 10 inches, and the angle is 9 degrees. First, the sine of 9 degrees must be calculated, which is approximately 0.1564. Then, multiplying this sine value by the length of the sine plate gives:

[ H = 10 \times \sin(9^\circ) ]

[ H = 10 \times 0.1564 ]

[ H = 1.564 \text{ inches} ]

This calculation confirms the gage block height as approximately 1.5643 inches, making it the correct answer. The other options do not match this computed value for the gage block height at the given angle and sine plate length.