Packet 8: Bonus 5
A law named for this trigonometric function relates this function of a triangle’s angles to their corresponding side lengths. For 10 points each:
[10e] Name this function, which in right triangles is equal to opposite over hypotenuse.
ANSWER: sine [or law of sines; or sine law]
[10h] The law of sines states that each side length divided by the sine of the opposite angle in a triangle is equal to two times this value. This value is equal to half the length of the hypotenuse for a right triangle.
ANSWER: circumradius [prompt on R]
[10m] Two New Orleans high schoolers used the law of sines to perform this task, which was once thought impossible without circular reasoning. Other approaches to this task involve rearranging triangles to fit within the area of a square.
ANSWER: proving the Pythagorean theorem [or proving a 2 +b 2 =c 2 ]
<Math — Andrew Gao> | SHOW-ME Four Packet 8
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 23 | 14.35 | 96% | 39% | 9% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Detroit Catholic Central A | Williamston | 10 | 0 | 0 | 10 | E |
| Detroit Catholic Central C | Utica Academy | 10 | 0 | 0 | 10 | E |
| Hillsdale Academy A | Traverse City Central A | 10 | 0 | 10 | 20 | EM |
| Hillsdale Academy B | Holt | 10 | 0 | 0 | 10 | E |
| Hillsdale Academy C | Detroit Country Day B | 10 | 0 | 0 | 10 | E |
| New Boston Huron | Traverse City Central B | 10 | 0 | 0 | 10 | E |
| New Buffalo A | Rockford B | 10 | 0 | 0 | 10 | E |
| Okemos A | Detroit Catholic Central B | 10 | 0 | 10 | 20 | EM |
| Okemos B | Detroit Country Day A | 10 | 10 | 10 | 30 | EHM |
| Troy A | Hillsdale Academy D | 10 | 0 | 0 | 10 | E |
| U of D Jesuit | Troy B | 10 | 0 | 0 | 10 | E |
| White Cloud A | Rockford A | 10 | 0 | 0 | 10 | E |
| White Cloud B | Taylor | 10 | 0 | 0 | 10 | E |
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| Rube Goldberg XIX | 11/20/2025 | ✓ | 13 | 13.08 | 100% | 23% | 8% |
| SHOW-ME Four Nationwide HS | 11/20/2025 | ✓ | 5 | 18.00 | 100% | 60% | 20% |
| SPOOKY IX | 11/20/2025 | ✓ | 5 | 14.00 | 80% | 60% | 0% |