For the first half of today's tutorial, we will go over a few of the
most common mistakes and misconceptions seen on the midterm exam.
These concerned (at a high Level):

- Some modules
Take a look at the three files
dtrig.scm,
module-tests.scm
triangles.scm.
`dtrig.scm`

provides the three basic trigonometry functions
(sin, cos, tan) to work with angle measures given in degrees rather than
radians. `module-tests.scm`

provides just one function which
will take a name and a series of tests and will run the tests, using output
to indicate passing/failure. This allows one way to write tests in modules.
The file `triangles.scm`

provides a few classes to represent
triangles. Note that this module *requires* the other two. Make sure
you understand how these modules are set up.

- Class hierarchy: triangles
The
`triangle%`

base class represents any triangle and
has the four operations
`sides`

, `perimeter`

, `area`

,
and `shortest-side`

. `sides`

returns a list of the
lengths of the triangle's three sides, and the other three do what we would
expect. Only the `sides`

method is not implemented in the base
class.

There are three subclasses of `triangle%`

:
`scalene%`

, `isosceles%`

,
and `equilateral%`

. These represent the different types of
triangles as one might expect, and `equilateral%`

is a subclass of `isosceles%`

(why?).

Override the `area`

function in `isosceles%`

with
a more efficient version that takes advantage of the fact that the area of
an isosceles triangle is equal to the square of the repeated side length times
the sine of the angle between them, divided by 2. Then override the
`shortest-side`

function in `equilateral%`

with
a more efficient version (easy).

Next, make a new class `right%`

(for right triangles),
and add it to the module. The initialization should take the lengths of the
two sides around the 90-degree angle, and the class should override the
functions `sides`

and `area`

, as well as add a new
function `hypotenuse`

. Be sure to add tests for the new class.

- Using a module
In a new file, load the triangles module and write a new function,
`obtuse?`

, which consumes an instance of any triangle class, and
produces true if and only if that triangle is obtuse, i.e., it has an angle
larger than 90 degrees. You might want to use the fact that this is only true
if the square of the longest side is strictly greater than the sum of the
squares of the other two sides.