Answer:

Step-by-step explanation:
Let determine the angles behind each trigonometric expression:


Given that
, the value of
is:



Given that
, the value of
is:

The sine function of the sum of angles can be determined by the following identity:

If
and
, then:


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Given:
Radius of the circle = 6 inches
Central angle = 75 degrees.
To find:
The length of subtended arc, i.e., x.
Solution:
The formula for arc length is:

Where, r is the radius and
is the central angle.
Putting
in the above formula, we get




Therefore, the value of x is 7.9 inches.
Step-by-step explanation:
Answer in attached image...
hope it helps