Your friend Tyler is preparing to climb a rock face and wants to figure out how far he will need to climb to reach one of three different peaks.  You remember a trick you can use to help him out.

Assignment Task

Your Peak of Choice

Your friend Tyler is preparing to climb a rock face and wants to figure out how far he will need to climb to reach one of three different peaks.  You remember a trick you can use to help him out.  You realize that if you place a small mirror on the ground and move it to where Tyler can see the reflection of the peak in the  mirror, then the angles from the mirror to Tyler and from the mirror to the peak are congruent. 

The image below displays the three peaks with information about Tyler’s measurements.  Tyler is 6 feet tall.

Have you ever gone rock climbing?  If so, describe your experience.  If not, would you like to? To help Tyler identify the heights of the peaks, write down what you know about each peak from the first page of this activity Choose one of the three peaks.  On the diagram below, label the distances.  Are these triangles similar, congruent, or neither?  Explain your answer. Based on the information above, Tyler has created three proportions to help identify the heights of the peaks.  Complete the chart below to analyze his work and identify any errors. Create a problem that can be solved using similar triangles.  You may use the internet to gather ideas, but your question should be unique.  Be sure to include a list of any websites you used. 

            Your problem must include:

A real world situation involving similar triangles.A question that can be answered using the similar triangles.All information needed to answer the question.Diagrams and/or pictures if needed.A list of websites used to gather ideas.Create an answer key for your problem in question #6.  Be sure to show all steps so the grader does not get confused!