Suppose that angle J and angle K are complementary, and that the measure of angle J is 48 degrees, 26 minutes, 8 seconds. What is the measure of angle K?
90° - 48°26'8"
To find the measure of angle K, we need to subtract the measure of angle J from 90 degrees (complementary angles add up to 90 degrees).
Here is the calculation step-by-step:
1. Convert 48 degrees, 26 minutes, 8 seconds to decimal degrees.
- 26 minutes = 26/60 = 0.4333 degrees
- 8 seconds = 8/3600 = 0.0022 degrees
- Total = 48 + 0.4333 + 0.0022 = 48.4355 degrees
2. Subtract the measure of angle J from 90 degrees.
- 90 degrees - 48.4355 degrees = 41.5645 degrees
Therefore, the measure of angle K is 41 degrees, 56 minutes, 8 seconds.
To find the measure of angle K when we know that angle J is 48 degrees, 26 minutes, and 8 seconds, we need to understand that when two angles are complementary, the sum of their measures is 90 degrees.
In this case, angle J is given as 48 degrees, 26 minutes, and 8 seconds. To convert the minutes and seconds to decimal form, we divide each value by 60. Here's how we calculate it:
48 degrees + (26 minutes / 60) + (8 seconds / 3600)
Converting the minutes and seconds to decimal form:
48 degrees + (26 / 60) degrees + (8 / 3600) degrees
To simplify:
48 degrees + (0.43333) degrees + (0.00222) degrees
Adding all the values:
48.43555 degrees
Now, we know that the sum of angle J and angle K is 90 degrees, so:
Angle K = 90 degrees - 48.43555 degrees
Calculating:
Angle K = 41.56445 degrees
Therefore, the measure of angle K is 41 degrees, 33 minutes, and 52 seconds.