Text Box: ADVENTURES IN TRIGONOMETRY

                                                                                                                              By   Anna DeConti

                                                                                                                              NCSSM

                                                                                              

You and your friend, Josh, are in New York City during your spring vacation.   You have never been there and find it so exciting.   You are walking down a side street on your way to see if you can get tickets for a play on Broadway, and, all of a sudden, a brown manila envelope drops in front of you.   You pick up the envelope not knowing what it could possibly contain or to whom it may belong.   You and Josh look all around and even up at the windows on the buildings surrounding the area and do not see anyone who looks like they might have lost it.   What should you do?

 

You look at the front of the envelope and it has printed in bold type:

 

You have won a prize

Open this to find a clue

 

Josh says, “Throw the envelope away!”   But, you say, “No, let's open it up and see what it says.   We have some time before we can purchase tickets for a theater performance.” Josh agrees and you tear open the envelope.   Inside is a slip of paper with the following.

Go to the box office at the Palace Theater and ask for the tickets under the name of John Wallis

 

You both decide that maybe there would be tickets waiting and you can see a play for free.   So you go to the box office and ask for the tickets for “John Wallis”.   You are handed an envelope which has two tickets for today's show and a typewritten note.

 

This is the beginning of your great adventure. If you continue to follow the clues you will be given a prize when you finish.   You will need to know some trigonometry to continue your quest.

 

You and Josh state that you are getting good grades in Trig this semester, and this idea seems to be really neat - especially since there will be a prize at the end.

 

On the back of this note you find the following directions.

 

Inside the theater there are five posters one of which has a small hole in which I have placed a piece of paper. On the paper are clues and directions on how you may get your prize.

You and Josh decide to see the show first before you look for the poster.   However, as you walk to your seats, Josh asks, “How do we find the small hole?   There are at least 10 posters in this lobby and three in the upstairs one.” You are dejected to think that you were not given enough information to gain your prize.   You respond “Oh well, at least we will see the play.”   As you are ushered to your seats, you are given a program.   When you open the program a paper falls out which reads as follows:

 

To find what you are looking for solve the following problem:   Write down the answer, in words, as well as the units.

 

Click below to view the problem.    

Theater Poster Problem

 

 

Aha!!!!   You and Josh have solved the problem and are ready to get your clue.  You, being the good student that you are, write down the answer to the problem and put it in your pocket.  Josh asks, “What poster has our clue?”   You think for a minute and both of you smile.   The one that was in the problem!!!!!

 

You need a chair to reach the hole.   And after a few minutes, you find the hole and the piece of paper that was inserted.   No one sees you because the poster is somewhat hidden from view of the theater employees.

 

Josh anxiously unfolds the paper.   It reads:

  Get on the subway across the street and take it to Coney Island .   At the ticket station for the Ferris wheel, you will find tickets for 2 rides and further directions.   Remember to use the name: John Wallis.

 

Now you and Josh look for the subway.   Yes!   There is a subway across the street next to the restaurant!!   You run down the steps, anxious to get to your next destination!   This adventure is turning out to be great!!!   We will get to see Coney Island and ride a Ferris wheel.  

 

You have no trouble locating the train to Coney Island , getting your ticket and finding a seat.   It doesn't take too long to get there.   You find your way to the ticket booth and ask for the tickets for John Wallis.   At first, the attendant doesn't understand what you want, but the manager comes along and helps him find the appropriate envelope.  

 

Josh says “I'll open the envelope this time.”   And he rips it open to find two tickets for the Ferris wheel.    You say, “OK, this is great!!!! “What will happen next?”   As the attendant opens the bar for you to sit down, you and Josh see a piece of paper taped to the seat with the following written on it:

 

When you get off the roller coaster, use your answer to the problem to walk the number of paces, due east of the ticket booth, in order to find something which will help you claim your prize.   Round your answer to the nearest whole number and write it down in words, with its units.

 

Double click below to view the problem

 

Ferris Wheel Problem 

 

 

You comment, “This is a pretty difficult problem.   But I think I know how to solve it.   First we need to find the equation of the sinusoid.   I think we can do that.   Our trig teacher taught us how to do these equations.”

 

You solve the problem and once you finish Josh states, “That required some work, but I think we have the right answer.   Let's walk those steps.   Now which way is east?”

             

When you finish walking you arrive at a concession stand.   “What do we do now?”   You ask.   Josh looks down and finds an 8.5” x 11” sheet of paper tacked to the front of the stand – it reads:

 

You are getting closer to your prize!!!!   Go to Battery Park and take the Ferry which goes to the Statue of Liberty .   At your hotel, you will find the tickets for your trips.

 

You and Josh are very tired from your adventures for the day and go back to the hotel to tell everyone about your adventure and what you plan on doing the next day.   Because you are on a school trip, your friends listen to your tale in awe - to think that you got to go to a play and see Coney Island for free and tomorrow you will have another adventuresome day.   And, when you finish, you will get a prize!!!!   They are all somewhat jealous.

 

The next morning you and Josh pick up your tickets for your trip – ironically, they are in your names!!!!   You then take the subway to the dock at Battery Park and board the ferry to the Statue of Liberty.

 

As you and Josh leave the ferry a steward appears and hands you an envelope which states the following:

 

When you solve the following problem go to the helicopter which has been hired especially for you. Permits have been secured – so don't worry.   Tell the pilot the number of miles you need to go and he will take you there.   He knows the direction.    You will be heading towards a pleasure boat and will cruise around New York City for the rest of the day.   Round your answer to the nearest whole number and write it down in words, with its units.

 

Click below to view the problem

Boat Problem

 

“Wow!” You and Josh say together.   “This problem is not bad.”   After you solve the problem you hand the helicopter pilot your answer, get in the helicopter and off you go.   What a beautiful view of the city!!!!   As you approach the pleasure craft, you see all your friends from the trip on the boat!   How great!!   You will be able to tour with your friends.   But you ask yourself, who invited them to come on this boat?   This is quite puzzling to both you and Josh.   Oh, well.   We will just enjoy the trip and view!!!

 

The trip takes several hours and you both have lots of fun!!!!   You all go back to the hotel together.   As you are walking into the hotel, your best friend hands you an envelope with a letter, tickets   and a 5 dollar bill enclosed.   You unfold the letter and read:

 

You have done very well.   This afternoon you will visit the Empire State Building .   You can walk there from the hotel.   Go up to the 86th observation floor.   Once there, find a woman with a white flower in her hand.   Give her the $5 and she will give you the last clue to your prize.   In this clue you need to find the distance to a strange looking taxi which is due south of the building.   Round your answer to the nearest whole number and write it down in words, with its units.

 

You find the woman.   She hands you a scrap of paper on which is written the following:

 

Click below to view the problem

Empire State Building Problem

 

You and Josh find the taxi in your spot finders and it is surely strange looking!   You have no difficulties solving the problem, and you walk to the cab!   As you get in you see that the driver's name is John Wallis.   Before you can say anything he hands you an envelope which says

TO THE FRIENDS OF

JOHN WALLIS

 

  He quickly drives off.     You open the envelope and find the following inside and decide to wait until you got back to the hotel before you work on it.   Now you can claim your prize!

 

The person who will give you your prize can be found by doing the following:

1.   Write your answers (rounded to the nearest whole number) to each clue in words.   Put one letter in each block in the grid below and do not put any spaces between the letters.

 

Clue 1    Poster

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Clue 2   Ferris Wheel

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Clue 3   Boats

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Clue 4   Empire State Building

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.   Cross out the following letters and words:

            a. The units on clues two, three and four (ex. miles)

            b. Each of the following number of letters:

                                          5 - T's

                                          3 – H's

                                          2 – I's

                                          4 – E's

                                          4 – N's

                                          2 – S's

                                          2 – F's

                                          1 - W

                                          3 – O's

                                          1 - U

                                          1 - D

 

 

              c. Unscramble the letters to find who will give you your prize!

 

By the way – who is John Wallis?