Video Transcript
Find the measure of angle 𝑋 in
degrees given that two times cos of 𝑋 equals the tan of 60 degrees, where 𝑋 is an
acute angle.
Since 𝑋 is an acute angle, we’re
only interested in solutions in quadrant one. So, we can look at two times cos of
𝑋 is equal to tan of 60 degrees. And the first thing that we can do
is solve for tan of 60 degrees, which is equal to the square root of three. Because this is an angle that we
usually memorize, you maybe already knew that the tan of 60 degrees was the square
root of three. If not, you could plug that into
your calculator. Now, we have two times cos of 𝑋
equals the square root of three. Our goal is to solve for 𝑋. We’re trying to get 𝑋 by
itself. So, we divide through by two and we
see that the cos of 𝑋 has to equal the square root of three over two.
And one of two things can happen
here. You might remember that the cos of
30 degrees is the square root of three over two. Or you might recognize that we can
solve for 𝑋 by finding the inverse cosine of both sides of this equation. The inverse cos of the cos of 𝑋
equals 𝑥 and the inverse cos of the square root of three over two can be plugged
into a calculator, which will return 30 degrees. If you knew that the cos of 30
degrees was the square root of three over two, you would recognize that 𝑋 has to be
equal to 30 degrees. But both methods prove this.
