To find the approximate measure of the angle [tex]\( A \)[/tex] in degrees when given [tex]\(\sin A = 0.6486\)[/tex], follow these steps:
1. Calculate the Inverse Sine (Arcsine):
- The sine of angle [tex]\( A \)[/tex] is given as 0.6486. To find the angle [tex]\( A \)[/tex], we need to use the inverse sine function (also called arcsine), represented as [tex]\(\sin^{-1}\)[/tex] or [tex]\(\arcsin\)[/tex].
- Using a calculator, find [tex]\(\arcsin(0.6486)\)[/tex]. This will give us the angle [tex]\( A \)[/tex] in radians.
- The angle [tex]\( A \)[/tex] in radians is approximately 0.7057 radians.
2. Convert Radians to Degrees:
- To convert from radians to degrees, use the conversion factor [tex]\(180^\circ / \pi\)[/tex].
- Using this conversion, the angle [tex]\( A \)[/tex] in degrees is approximately 40.4361 degrees.
3. Round to One Decimal Place:
- Finally, round the angle [tex]\( A \)[/tex] to one decimal place.
- The rounded angle [tex]\( A \)[/tex] is [tex]\( \boxed{40.4} \)[/tex] degrees.
So, the approximate measure of the angle [tex]\( A \)[/tex] is [tex]\(40.4\)[/tex] degrees, rounded to one decimal place.
