Video Transcript
Given that 𝐴 is an acute angle and
sin 𝐴 is equal to 0.8193, determine the measure of angle 𝐴 to the nearest tenth of
a degree.
We know that sin of some unknown
angle 𝐴 is equal to 0.8193. If we think about this trig
function, the 𝜃-value is an angle measure, and it’s equal to some ratio of side
lengths. If we know the ratio of side
lengths and we want to know the angle measure, we need a function that can undo the
sine function, and that would be the sin inverse of the sin 𝜃. We’ll need to take the inverse sin
of sin 𝐴. So, we’ll do that to both sides of
our equation. The sin inverse of sin 𝐴 is just
equal to 𝐴, and the sin inverse of 0.8193 can be found with a calculator. Make sure that your calculator is
set to degrees, since we’re interested in this angle measure in degrees.
When we do that, we get 55.0147
continuing degrees. We’ll round this to the nearest
tenth, and we’ll see that the measure of angle 𝐴 is 55.0 degrees. We’ve been given that 𝐴 is an
acute angle, and so we’re only interested in the smallest value that 𝐴 can be,
which here is 55 degrees.
