Expert: Josh - 11/17/2007

Question
If two angles of a triangle have the measurements of 92 degrees 17 minutes 23 seconds and the other angle 37.8425 degrees, what is the last angle in the triangle.  Give the measure in degrees, minutes, and seconds.

Answer
Jennifer,

To answer this question, we need to know two things:
1) The angles inside a triangle add up to 180 degrees. So, the third angle is 180-(37.8425+x), where x is the first angle measured in degrees.
2) We need to convert 92 degrees 17 minutes and 23 seconds to degrees. The angular units are analogous to the time units.

TIME         ANGLE
60 min/hr    60 min/deg
3600 sec/hr  3600 sec/deg

Thus, the angle "x" mentioned in (1) is given by 92 + 17/60 + 23/3600. I will let you simplify this expression to a decimal figure.

Applying the result in (1), the third angle is given by 180-(37.8425+x).

You can use the remainder theorem to convert this to degree, minute and second.

e.g., Suppose the third angle y = 45.25027778 degrees.
We obviously have 45 degrees from the integer part. Dividing the fractional part 0.25027778 by 1/60, we get 15.017. Rounding this down to the nearest integer, we have 15 minutes. The remainder is given by 0.017. Dividing this by 1/60 again, we get 1. So, 45.25027778 degrees is equivalent to 45 deg 15 min 1 sec.

Good luck!