Astronomers sometimes use angle measures divided into degrees, minutes, and seconds. One degree is equal to 60 minutes, and one minute is equal to 60 seconds. Suppose that <J and <K are complementary, and that the measure of <J is 48 degrees, 26 minutes, 8 seconds. what is the measure of <K.
It is unfortunate that measurement of angles, and time, has escaped the metric system.
Things would be so much easier.
K = 90° - 48° 26' 8"
= 89° 59' 60" - 48°26'8"
= 41° 33' 52"
Hint:
If you have a good scientific calculator, look for key labeled
D°M'S
it will do all your calculations in base 60
enter
90 DMS
-
48 DMS 26 DMS 8 DMS
=
and voila! there is your answer
btw, that same key can be used to do arithmetic of addition/subtraction of different times.
e.g. 5:12:45 + 4:55:12
= 10:07:57
this did not help!!!!!!!!!!!!!!!
answer answer
The answer is 41 degrees and 52 seconds.... borrow 1 from the complementary 90 degrees and make it 89 degrees and 60 mins subract the 48 degrees and 8 seconds -48 26 mins 8 seconds
To find the measure of angle K, we first need to understand how to convert between degrees, minutes, and seconds.
1 degree is equal to 60 minutes, and 1 minute is equal to 60 seconds. Therefore, we can convert from degrees to minutes by multiplying the degree value by 60, and from minutes to seconds by multiplying the minute value by 60.
Given that the measure of angle J is 48 degrees, 26 minutes, and 8 seconds, we need to convert this to a single unit, such as degrees.
First, let's convert the minutes and seconds to degrees:
48 degrees + (26 minutes / 60 minutes per degree) + (8 seconds / 3600 seconds per degree)
= 48 + (26 / 60) + (8 / 3600)
= 48 + 0.4333 + 0.0022
= 48.4355 degrees
Now, since we know that angle J and angle K are complementary, the sum of their measures is 90 degrees.
Let's denote the measure of angle K as x.
48.4355 degrees + x = 90 degrees
To find x, we subtract 48.4355 degrees from both sides of the equation:
x = 90 - 48.4355
x = 41.5645 degrees
Therefore, the measure of angle K is approximately 41.5645 degrees.