Question

two angles of a triangle are 72 degree 53 minutes 51 seconds and 41 degree 22 minutes 50 seconds respectively. Find the third angle in radians.

Answer 1

The sum of all angles in a triangle is 180 degrees.
1 degree = 60 minutes
1 minute = 60 seconds.
Therefore the third angle must be
》 180 deg - the measure of the two given angles
Deg Min Sec
180 0 0
-72 53 51
---------------------------
107 deg 6 min 9 sec
- 41 deg 22 min 50 sec

= 66 deg 43 min 19 sec

Now 180 deg = pi radians
》 1 deg = pi/180 radians
》 1 min = pi/(180*60) radians
》 1 sec = pi/(180*60*60) radians

Hence the measure of the angle is 66*pi/180 + 43*pi/(180*60) + 19*pi/(180*60*60)
The answer is (240199*pi)/648000 radians
Which is approximately
1.1645 radians