# Puzzling Pentagon?

Directions: Using the digits 1 to 9 and the math operations of +, -, ÷, ×; create expressions for the sides of the following pentagon where A > C > B.

What can you say about angles a and b?

What are the measures of a and b?

How do you know your answers are correct?

Are there any other solutions?

# Trig Ratios- Open Middle Problem

Directions: Using the following trig ratios, complete the following table:

cos 30º, sin 30º, cos 45º, sin 45º, tan 30º, cot 30º, sec 30º, csc 30º

What trig ratios CANNOT go in the center square?

What is the smallest trig ratio that can be placed in the center square?

# Trig Ratios

Consider the following figure:

What values of x, y and z will produce the following inequality?

csc B < sec B < tan B < sin B < cot B < cos B

How does the inequality

sin B < tan B < cos B < cot B < csc B < sec B

change your diagram, values or thinking?

# Trig Functions- Open Middle Problems

Directions: Fill in the empty blanks so that you create a triangle whose Cos Θ = √2/2. You can use whole numbers 1 through 9, but can only use a number once: (5, 4), (__,__) and (__,__)

# Right Triangle Similarity- Open Middle Problem

Directions: Using the numbers 1 to 9 and math operations of (+, -, x, ÷), how many different triangles can you create where tan Θ=.75?

Note: you can only use each number once per triangle created.

# Rectangle Partitions- Open Middle Problem

Directions: Using the numbers 1 to 9, using each number only once, complete the following statement:

___ rows and ___ columns create a rectangle of ___ units

1. What different possibilities will your students come up with?
2. How many of these statements can you create?
3. How would increasing the interval from 1 to 19 change the problem?

# Rectangle Construction- Open Middle Problem

Directions: Using the following squares, how many different rectangles can you make?

How does adding 4 more squares change the problem?