Explain why the value of sine ratio for an acute angle of a right triangle must always be a positive value less than 1

In this exercise we have to explain why the sine value must always be positive, for this is because of the first quadrant.

The sine of an angle will always be positive in the 1st and 2nd quadrants and negative in the 3rd and 4th, always under the ordinate (y) axis.

In this way we can say that this occurs because:

Will be positive because it is an acute angle so the triangle when plotting in the unit circle would only be in the first quadrant. All values in the first quadrant are positive.

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answer would be 8.64 or s = 11π/4 inches

step-by-step explanation:

s = r θ  

where s = arc length  

r = radius = 3 inches  

θ = central angle in radians = ( π /180)*165  

s = 3(π/180)*165  

= 8.64 inches