A triangle has sides measuring 7 units and 9 units. The angle opposite the 7 unit side measures 32°. What is the measurement of the angle opposite the 9 unit side?
Hint
Apply the Law of Sines directly to the forehead.
Answer
42.9°
Example 2
A triangle has sides measuring 15 units and 20 units. The angle between them measures 75°. What is the measurement of the side opposite the 75° angle?
Hint
A problem with two sides, an angle, and then a third unknown side? Follow the Law of Cosines to victory.
Answer
21.7 units
Example 3
A triangle has angles measuring 87°, 32°, and 61°. If the side opposite the 87° angle is 22 units long, what is the length of the side opposite the 61° angle?
Hint
There's some extra information here. We don't need to know about the 32° angle to finish this problem.
Answer
19.3 units
Example 4
A triangle has sides measuring 6, 10, and 12 units. What is the measurement of the angle opposite the side that is 12 units long?
Hint
Follow the Law of Cosines.
Answer
93.8°
Example 5
A triangle has sides measuring 45 units and 43 units, with an included angle of 33°. What is the measurement of the side opposite the 33° angle?