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 46 degrees, 33 minutes, 51 seconds. What is the measure of ∠K?
To find the measure of ∠K, we need to subtract the measure of ∠J from 90 degrees (since ∠J and ∠K are complementary).
The measure of ∠J is given as 46 degrees, 33 minutes, 51 seconds.
Before subtracting, we need to convert the measure of ∠J into a decimal form.
1 degree is equal to 60 minutes, and 1 minute is equal to 60 seconds.
To convert ∠J into degrees only, we divide 33 minutes by 60 and add the result to 46 degrees:
46 + (33/60) = 46.55 degrees.
Next, we divide 51 seconds by 60 and add the result to 46.55 degrees:
46.55 + (51/3600) = 46.5608333 degrees (rounded to 7 decimal places).
Now, we can subtract the measure of ∠J from 90 degrees:
90 - 46.5608333 = 43.4391667 degrees (rounded to 7 decimal places).
Therefore, the measure of ∠K is approximately 43.4391667 degrees.
90° - 46°33'51"
= 89°59'60 - 46°33'51°
= 43°26'9"