Special Triangle (II) 30-60-90
Interact with the applet below for a few minutes. After doing so, please answer the questions that appear beneath the applet.
Feel free to move the BIG PINK POINTS (A & B) anywhere you'd like prior to sliding the slider.
Note: If you're struggling to answer any of these questions, refer to your answers to the questions you completed in the lab that used the applet found here:
https://tube.geogebra.org/material/simple/id/3295791
Questions:
1) How would you classify triangle ABC by its sides?
2) What is the measure of each gray angle? Explain why your answer is true.
3) What is the measure of angle ACO? Explain how you know this is true.
4) What is the measure of angle A? Give 2 reasons why your answer is true.
5) What are the measures of the interior angles of triangle ACO?
6) How does the length of the longest side of triangle ACO compare to the length of triangle ACO's shortest side? Explain how you know this to be true without referencing the last few actions within the applet.
7) Suppose AO = 3. What is the value of AC?
8) Given that AO = 3 and your response to (7) above, solve for the length CO. If necessary, write your answer in simple radical form.
9) Answer questions (7) - (8) again, this time with AO = 4.
10) Answer questions (7) - (8) again, this time with AO = 5.
11) Answer questions (7) - (8) again, this time with AO = 6.
12) Answer questions (7) - (8) again, this time with AO = 7.
13) Notice any patterns in your data above? If so, explain the relationships you've discovered as best as you can.
14) Answer questions (7) - (8) again, this time with AO = x. (Be sure your responses to these questions are expressions written in terms of x.)