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

To determine the appropriate gage block height for setting an angle of 9 degrees on a 10-inch sine plate, it’s important to understand how the sine plate functions. A sine plate uses the trigonometric sine function to establish angles. The sine of the angle in this case informs us about the height of the gage block needed to achieve that specific angle.

The formula used to calculate the height of the gage block is given by:

[

\text{Height} = \text{Length} \times \sin(\theta)

]

where:

• Length is the length of the sine plate, which is 10 inches in this case,

• (\theta) is the angle in degrees (9 degrees).

Next, we need to convert the angle from degrees to radians, as most calculators use radians for trigonometric functions. However, since the sine function can often be computed directly in degrees in many calculators, we can proceed straightforwardly by finding the sine of 9 degrees.

Calculating:

[

\sin(9^\circ) \approx 0.1564

]

Plugging values into the formula gives:

[

\text{Height} = 10 \times \sin(9^\