To determine which pair of launch angles will result in two identical projectiles having equal ranges, we need to utilize the principle that for projectiles launched with the same initial speed, their ranges will be equal if their launch angles are complementary. Complementary angles are defined as two angles that add up to 90 degrees.
Let's analyze each pair of angles to see if they add up to 90 degrees:
1. Pair A: 19.24°, 80.54°
- [tex]\( 19.24° + 80.54° = 99.78° \)[/tex]
- This pair does not add up to 90 degrees.
2. Pair B: 16.42°, 74.58°
- [tex]\( 16.42° + 74.58° = 91.00° \)[/tex]
- This pair does not add up to 90 degrees.
3. Pair C: 60.23°, 29.77°
- [tex]\( 60.23° + 29.77° = 90.00° \)[/tex]
- This pair adds up to 90 degrees, making these angles complementary.
4. Pair D: 89.53°, 01.47°
- [tex]\( 89.53° + 01.47° = 91.00° \)[/tex]
- This pair does not add up to 90 degrees.
5. Pair E: 42.42°, 47.59°
- [tex]\( 42.42° + 47.59° = 90.01° \)[/tex]
- This pair is very close but does not add up exactly to 90 degrees (allowing for a small tolerance, they are not exactly complementary).
Given that the only pair that adds up exactly to 90 degrees is Pair C, the correct answer is:
C. 60.23°, 29.77°
