Final answer:
The third angle of a triangle, with the other two angles given as 33° 47' and 93° 49', measures 52° 24'. This is found by subtracting the sum of the given angles from the total of 180 degrees, which is the sum of angles in any triangle.
Step-by-step explanation:
The measure of the third angle in a triangle can be found by knowing that the sum of all angles in a triangle is 180 degrees. Given two angles of a triangle, 33° 47' and 93° 49', we first convert the minutes to degrees by remembering that 1 minute is 1/60th of a degree. Therefore:
- First angle in degrees: 33° + 47'/60 = 33.7833°
- Second angle in degrees: 93° + 49'/60 = 93.8167°
Adding both angles gives us a total of 127.6°. Subtracting this from the total 180° available in any triangle provides the measure of the third angle:
180° - 127.6° = 52.4°
Since we need the answer in degrees and minutes, we need to convert the decimal back to minutes. There are 0.4 degrees in the remainder which is equivalent to 0.4*60 minutes = 24 minutes.
Therefore, the third angle measures 52° 24'.