options: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Explain and use the relationship between the sine and cosine of complementary angles.
problem_activity: Task
Below is a table of diameters of different denominations of United States
Coins:
| Denomination | Diameter  |
|--------------|-----------|
|     Dime     | $17.9$ mm |
|    Nickel    | $21.2$ mm |
|   Quarter    | $24.3$ mm |
| Half Dollar  | $30.6$ mm |
If we place nickels around a central dime, as in the picture below, there is room
for five nickels with extra space but not enough room for a sixth nickel:
[IMG]
How many dimes fit around a central dime?  What about around a
central nickel, quarter, or half dollar?  Do the dimes fit snugly or is there
extra space?
How many half dollars fit around a central dime?  What about around
a central nickel, quarter, or half dollar?  Do the half dollars fit snugly or
is there extra room?
Extending the work in (a) and (b) above, for positive numbers $r$ and $s$
how many circles of radius $s$ will fit around a central circle of radius $r$?


correct_option_index: 1