Video Transcript
Find, to four decimal places, the
value of tan 38 degrees, 48 minutes.
In this question, we’re asked to
find the tangent of an angle given in degrees and minutes. One way to do this is to begin by
converting our angle into a measure in just degrees. We recall that one degree is equal
to 60 minutes. This means that 48 minutes is equal
to 48 over 60 degrees. The fraction 48 over 60 can be
simplified by dividing the numerator and denominator by six. This gives us eight over 10 or
eight-tenths. And we can write this as a decimal
as 0.8. 48 minutes is therefore equal to
0.8 degrees. This means that 38 degrees and 48
minutes can be rewritten as 38.8 degrees.
We need to find the tangent of this
angle, and we can type this directly into our calculator. Ensuring that we are in degree
mode, we have an answer of 0.804020 and so on. In order to round this to four
decimal places, we consider the fifth digit after the decimal point. As this is a two, we round
down. The tan of 38.8 degrees, and
therefore the tan of 38 degrees and 48 minutes, is equal to 0.8040 to four decimal
places.
It is worth noting that on many
calculators there is a degrees, minutes, and seconds button that we can use to
directly type the expression in this question into the calculator. Either method would give us the
same answer correct to four decimal places.
