# UTPA STEM/CBI Courses/Algebra/Right Triangle Problems

Course Title: Intermediate Algebra
Lecture Topic: Right Triangle Problems
Instructor: Rommel Garza
Institution: South Texas College

## Backwards Design

Course Objectives
* Primary Objectives- By the next class period students will be able to:
** Identify a Right Triangle problem
** Setup an equation to solve the Right Triangle problem
** Solve a Right Triangle problem
* Sub Objectives- The objectives will require that students be able to:
** Set up real world problems involving radical equations.
** Solve Radical Equations.
* Difficulties- Students may have difficulty:
** Recall the formula needed for Right Triangle Problems, Pythagorean Theorem a$^2$+b$^2$=c$^2$
** Set up the radical equation
** Finding exact answers to radicals
** Finding approximate answers to radicals
** Rounding numbers to the nearest tenths, hundredths, etc...
* Real-World Contexts- A variety of real world problems translate into right triangle problems. There are many ways students can use this material in the real-world, such as:
** Determining the height of buildings, height of trees, height of an antenna etc.
** Determining the distance between two points
** Builders laying the foundation for the corners of a building
Model of Knowledge
* Concept Map
** To accurately make a 90 degree angle using Pythagorean Theorem
* Content Priorities
** Enduring Understanding
*** Solving real life application problems that require radical equations
** Important to Do and Know
*** Simplifying radicals
*** Approximating radicals
** Worth Being Familiar with
*** Pythagorean Theorem
*** Names of the sides of a right triangle
Assessment of Learning
* Formative Assessment
** In Class (groups)
*** Students work in groups on selected right triangle problems and present it to the entire class
** Homework (individual)
*** Students work on assigned problems and bring the difficulties to the next class
* Summative Assessment
** In class quiz over the lesson

## Legacy Cycle

OBJECTIVE
By the next class period, students will be able to:
* Identify radical equations
* Set up application problems involving radical equations
* Solve Radical Equations and applications.
The objectives will require that students be able to:
* Identify a right triangle problem
* Use the Pythagorean theorem to solve the right triangle problem
* Solve the radical equation for a right triangle problem
THE CHALLENGE
STC will be hosting a women's fast pitch softball game. You and your team members have been asked to use their multi-purpose sports field and set up the bases for the softball diamond. You are limited to the use of rope and a 100 ft measurement tape.
GENERATE IDEAS
How would we be able to find solutions for this type of problem?
MULTIPLE PERSPECTIVES
* Research surveying
* Pythagorean Theorem
* Radicals
RESEARCH & REVISE
Gather information about a women's fast pitch softball diamond
TEST YOUR METTLE
* Do a smaller scale experiment and see if we can relate the solution to a bigger scale.
* Write a procedure for laying out your own women's fast pitch softball diamond.
GO PUBLIC
Share & present their procedure for laying out a women's fast pitch softball diamond to the entire class.

## Pre-Lesson Quiz

* What is the relationship between the sides of a right triangle?
* If you know the length of two sides of a right triangle. What is the exact and approximate length of the third side?

## Test Your Mettle Quiz

* What is the approximate and exact length of the diagonal of a regulation soccer field?