### Video Transcript

Find the measure of angle 𝐸 given
that the tan of 𝐸 equals 18.5845 and angle 𝐸 is an acute angle. Give your answer to the nearest
second.

Since we know that angle 𝐸 is an
acute angle, we know that we’ll only be dealing with values in the first
quadrant. We know that the tan of 𝐸 is equal
to 18.5845. We know that the tangent of some
angle equals a ratio of side lengths. And we also know that if we’re
given a ratio of side lengths for some tangent, using the inverse tangent, we can
find the angle measure. And that means we’ll want to take
the inverse tangent of both sides of this equation. The inverse tan of tan of 𝐸 equals
𝐸. And before we find the inverse tan
of 18.5845, we need to think about “are we dealing with radians or degrees?” We need to round this value to the
nearest second. A second is a fraction of minutes,
and a minute is a fraction of a degree. That means we’ll need to operate
this inverse tangent in degrees.

Making sure our calculator is set
to degrees, we get that 𝐸 equals 86.91998286 continuing degrees. This means 𝐸 has 86 whole degrees
and another partial degree. In order for to us to turn this
partial degree into minutes and seconds, we have to remember that one degree equals
60 minutes. And that means to find out how many
minutes 0.91998286 continuing degrees would be, we multiply by 60. And when we do that, we get
55.19897132 continuing minutes, 55 whole minutes and a partial minute.

Our final step will be converting
this partial minute into seconds. And for that, we have to know that
one minute equals 60 seconds. So, we have 86 degrees, 55 minutes
and then we’ll have 0.19897132 times 60 minutes, which gives us 11.93827 continuing
seconds. To round to the nearest second,
we’ll round that 11.9 up to 12. And we’ll say that the measure of
angle 𝐸 is equal to 86 degrees, 55 minutes, and 12 seconds.