Trigonometry Superbowl

Aimee Frame , Gabrea Bender

1

1

2

Department of Engineering, University of Cincinnati, Cincinnati, OH; 2 Newport High School, Newport, KY

Abstract

This lesson is intended to be a fun way to show how trigonometry can be used in a

real-world situation. The students are given a playbook in which some of the route

information is missing. They are asked to determine the missing information using

their knowledge of trigonometry and right triangles. The first play is completed as

a class with guidance from the instructor to familiarize the students with the

terminology and the idea of creating right triangles that can help solve the

problem. The class is then divided into groups to complete the rest of the

playbook. Once completed, the instructor can review the solution process as a

class, showing that there can be more than one way to solve the problem and

reach the correct answer. Afterwards, a short presentation on how this idea is

applied in other real-world applications is given.

Playbook Activity

Pos

Yard Line

Field Position

Pattern

QB

Own 30 yd

line

Own 30 yd

line

Center

a) 30 yd pass 45 to his left

10 yds left of

center

a) Runs 15 yds at 0o (straight)

b) ?

WR

Prerequisite Knowledge

Pythagorean Theorem

o

Basic Trigonometric Functions (SOH-CAH-TOA)

Sine

Cosine

Tangent

a) If the pass is to be completed, at

what angle does the WR need to run

to catch the ball?

b) How far does the WR run (total

yards)?

c) Where is the pass caught?

Solving Equations

Special Right Triangles (optional)

90o-45o-45o

90o-30o-60o

Conclusions

Goals

The purpose of this lesson is to show the students how trigonometry can be

applied to real-world problems. The students are given a set of football plays

which they need to complete in order for the play to be successful. Using the

given information and the basic trigonometry functions (sine, cosine, and

tangent), the students will be able to determine the unknown values that will

make the play a success. After applying trigonometry to football, extensions to

other real-world and engineering applications will be discussed.

Pos

Yard Line

Field Position

QB

Opp 20 yd line Center

Pattern

a) At what angle does the QB need

to throw to connect with the WR?

b) How far is the ball thrown?

c) Is it a touchdown?

a) Under pressure, runs 90o left

10 yds

b) ?

Opp 20 yd line 5 yds right of center a) Runs 30 yds 40o to his right

WR

Reflections & Modifications

Objectives

Pre/Post Assessment

Students will be able to:

Determine the right triangles in a real-world problem.

Use right triangle relationships to find the unknown length and angle

measurements.

1.Find the HEIGHT of the tree.

C las s A verag e - B ell 1

45o

State Standards

30 feet

2.Find the HEIGHT of the Eiffel Tower.

P re-Tes t

P os t-Tes t

8.09

650 m

Kentucky Core Content:

MA-HS-2.1.3: Students will apply definitions and properties of right triangle

relationships (right triangle trigonometry and the Pythagorean theorem) to

determine length and angle measures to solve real-world and mathematical

problems.

Ohio Standards:

Geometry and Spatial Sense Standard, Grades 8-10, I: Use right triangle

trigonometric

relationships to determine lengths and angle measures.

Geometry and Spatial Sense Standard, Grades 11-12, A: Use

trigonometric relationships to

verify and determine solutions in problem

situations.

Mathematical Processes Standard, Grades 11-12, J: Apply mathematical

modeling to workplace and consumer situations, including problem

formulation, identification of a mathematical model, interpretation of solution

within the model, and validation to original problem situation.

This lesson provides an interesting application for trigonometry, encouraging the

students to apply their knowledge a different manner. Most of the students

seemed to like the real-world application of football and were engaged throughout

the activity. Although it can be challenging to those students that are struggling

with the prerequisite knowledge, the use in a different setting may help their

understanding of the basic trigonometric functions. Finally, this lesson can be

extended to the concept of vectors and vector addition for use in a physics class.

30o

3.Find the ANGLE the 15 ft ladder makes with the

floor.

5.55

2.642.73

1

2.64

1.82

2

1.091.55

3

1.18

0.00

4

Total

4 ft

C las s A verag e - B ell 2

4.

Pos

Yard

Line

Field Position

Pattern

QB

50 yd line

5 yds right of

center

a) Runs backward 45o left to the 45

yd line

b) Throws 15o left

WR

50 yd line

15 yds left of

center

a) Runs 0 (straight)

P re-Tes t

P os t-Tes t

7.26

Pre-Test

The first three questions are good indicators of how well the students

understand the basic trigonometric functions

Students that did well on these questions were better able to figure out how

to apply the trigonometry functions during the activity

It may be a good idea to ensure that each group has a student that did well

on the pre-test

Playbook

Although there are five plays listed, there is not enough time in one class

period to get through all of them.

Complete the first play as a class

The terminology has to be explained well to help prevent confusion on the

remaining plays

Players face the end zone

Left/Right refer to how the players are facing

Angles are measured from x-axis to line

Show how to make right triangles by using the slanted lines as

hypotenuses

Explain that there is more than one way to solve the problems

May need to reconvene as a class periodically

For bigger classes, may not be able to get to all the groups individually

Can clarify any questions about terminology

Discuss/show different approaches to the problem

o

4.26

2.48

1.57

1

a) How far does the WR have to run to catch the football?

b) How far is the ball thrown?

c) Is it a touchdown?

2.48

1.43

2

1.78

1.26

3

References & Acknowledgments

0.52

0.00

4

Total

Project STEP is funded through NSF Grant # DGE058532.

http://www.eng.uc.edu/STEP/activities/

This lesson was adapted from Amy Dimmerlings Geometry Superbowl lesson