Simplify:

## Set 15

## Find sin A in Isosceles Triangle

Find a formula for sin A in terms of *b* and *c* only. (Note: △ABC is an isosceles triangle.)

## Mongoes Eat Booms

Suppose that each of the following statements is true:

Either flems are tall or mongoes are not dangerous.

Flems are not tall.

Which of the following conclusions must also be true?

- Mongoes eat booms.
- Mongoes do not eat booms.
- Flems are not dangerous.
- Mongoes are dangerous.
- None of these statements is a possible conclusion.

## Pickled Walnuts, Prof. Piltdown

On the assumption the following nine statements are factually correct, what conclusion, if any, can be drawn?

- Pickled walnuts are always provided at Professor Piltdown’s parties.
- No animal that does not prefer Beethoven to Mozart ever takes a taxi in Bond Street.
- All armadillos can speak the Basque dialect.
- No animal can be registered as a philatelist who does not carry a collapsible umbrella.
- Any animal that can speak Basque is eligible for the Tintinnabulum Club.
- Only animals that are registered philatelists are invited to Professor Piltdown’s parties.
- All animals eligible for the Tintinnabulum Club prefer Mozart to Beethoven.
- The only animals that enjoy pickled walnuts are those who get them at Professor Piltdown’s.
- Only animals that take taxis in Bond Street carry collapsible umbrellas.

## Tennis Ball Can Volume

In a can of tennis balls that is exactly three balls high, which is greater, the volume of the balls or the volume of the air around the balls? (Disregard the thickness of the balls.)

## Parallelepiped

A rectangular parallelepiped has edges with integral lengths *x*, *y*, and *z*. The sum of the lengths of all twelve edges is 72 inches. The sum of the areas of all 6 faces is 212 square inches. The volume of the solid is 144 cubic inches. Find the length in inches of a diagonal of this solid.

## Irregular Hexagon

Express the area of this figure in simplest radical form. There are two right angles, and four other angles that are marked as being congruent.

## Hexagon, Triangle Area

An equilateral triangle and a regular hexagon have perimeters of the same length. If the triangle’s area is 2 square units, what is the area of the hexagon? Unless you’re a budding John Von Neuman, it isn’t necessary to calculate areas and then divide. That’s the hard way.

## Parallelogram, Triangle Areas

In parallelogram ABCD, M and N are midpoints of sides AD and BC, respectively. DN intersects AB at P, CM intersects AB at Q, and DN intersects CM at O. If the area of parallelogram ABCD is 24 square cm, find the area of triangle QPO.

## Collinear Points on Circle

In a rectangular coordinate plane, any circle that passes through (-2, -3) and

(2, 5) cannot also pass through (1989, *y*). Find the value of *y*.