To find the measure of an acute angle [tex]\( Q \)[/tex] given that [tex]\( \sin(Q) = 0.91 \)[/tex], follow these steps:
1. Identify the given value: We know that the sine of angle [tex]\( Q \)[/tex] is 0.91.
2. Use the inverse sine function: To find angle [tex]\( Q \)[/tex], we need to use the inverse sine function, often denoted as [tex]\( \sin^{-1} \)[/tex] or [tex]\( \arcsin \)[/tex]. This function will give us the angle whose sine is 0.91.
3. Calculate the angle [tex]\( Q \)[/tex]: By applying the arcsin function, we find [tex]\( Q = \arcsin(0.91) \)[/tex]. This will give us an angle in radians, but since we need the angle in degrees, we convert the result from radians to degrees.
4. Convert the radians to degrees: The conversion from radians to degrees is essential since the angle measure is required in degrees. This conversion involves multiplying the radian measure by [tex]\(\frac{180}{\pi}\)[/tex].
5. Round the result: Once the angle [tex]\( Q \)[/tex] is calculated in degrees, round the result to the nearest tenth of a degree for better approximation.
Following these steps, we find:
- The exact measure of angle [tex]\( Q \)[/tex] is approximately 65.50535152858032 degrees.
- Rounding this to the nearest tenth, we get [tex]\( Q \approx 65.5 \)[/tex] degrees.
Therefore, the measure of [tex]\( Q \)[/tex], when approximated to the nearest tenth of a degree, is [tex]\( 65.5 \)[/tex] degrees.
