EXPLORING SIMILAR TRIANGLES BY WALEED MELISSA AND RAYMOND

EXPLORING SIMILAR TRIANGLES BY WALEED, MELISSA, AND RAYMOND John J. Pershing Intermediate School Fall 2006

PROBLEM E H ? ? ? 16 D 10 F G 5 J A. What is the ratio of EF to HJ? B. What is the ratio of similitude of the shape? C. If EF = 18. Find the perimeter of GHJ. Use the extended response in solving the problem

What You Need To Know 1. Key concepts about similar shapes 2. How to use similitude ratio to find the side of the shape 3. What is the formula of perimeter of a triangle 4. How to create an equation to solve for X 5. Why and how we should use an extended response to solve the problem

Step 1 The triangles are similar, so the corresponding sides form equal ratios • Perimeter of DEF = Side of DEF GHJ = 10 = 2 5 1

Step 2 DF = 10 = 2 GJ 5 1 The similitude ratio of the shape is 2 1

Step 3 Extended Response If EF = 18 the perimeter of DEF 44 = 2 , where X= the perimeter of GHJ x 1 X = the perimeter of GHJ

What we learned • We learned how to find similitude ratio. • We learned how to use similitude ratio to find the sides of the triangle. • We learned how to do the extended response to a question

Credits • We give credits to Mr. John and Ms. Visico for guiding us in figuring out the problem, • Thanks to Ms. Lewis for showing us her technical skills. • We give Raymond credit for keeping the group on task. • We give Melissa credit for recording our information. • We give credit to Waleed for presenting the project to the class.

SIMILAR SHAPES By Cristal, Wing Ho, Xi Lin, & Manuel John J. Pershing Intermediate School Fall 2005

OUR PROBLEM H E 16 G D 10 5 J F 1. What is the ratio of Similitude of EF to HJ? 2. What is the ratio of similitude of the shape? 3. If EF =18, find the perimeter of GHJ. We’ll use the extended response to solve this problem.

What we need to know … Concepts involving similar shapes n What is the similitude of a shape n How to find the perimeter n How to calculate the ratio and simplify it n How to solve a problem using the extended response method n

Steps in Problem Solving n n The triangles are similar so the corresponding sides are equal. DF/GJ = 10/5 = 2/1 , so then EF/HJ must be equal to 2/1. Any of the corresponding sides for similitude DF/GF = 2/1 , so the ratio of the similitude is 2/1. Perimeter of ` DEF = 10 = 2 Perimeter of GHJ = 5 = 1 If EF = 18, the perimeter of DEF = 44 units 44/x = 2/1 , where X = the perimeter of GHJ 2 X = 44 and the X = 22 is the perimeter of GHJ ( the solution)

What We Learned We learned how to find the similitude of the right triangles. n We learned that we can find the ratio of the missing numbers from similar shapes. n We learned how to use the extended response in solving problems. n

Credits Thanks to Cristal for recording. n Thanks to Manuel and Xi Lin for being the presenters of the project. n Thanks to Wing Ho Ng for being the leader of the group. n Thanks to Ms. Visico , Ms. Lewis , and Mr. John for teaching us and giving us a chance to use the computers to do math. n

The Leaning Tower of Depression By Imtashal Tariq Happy Alam Christian Castillo Angelo Romero

Problem A fire warden’s tower is 43 meters tall. The angle of depression from the window of the tower to a fire in the woods is 50. How far way from the base of the tower is the fire? Use the extended response in solving the problem.

What We Need to Know 1)We need to know the meaning of extended response. 2)We need to know the ratio to be used to solve the problem. 3)We need to know how to write tangent 850

Steps to Solving the Problem • Draw the shape and label it. • Use the calculator to find the decimal of tangent 850 • Cross multiply. • Estimate your answer to the nearest meter. 77 Tan 85=x/43 • • 11. 4300523=x/43 43(11. 4300523)= 43 m 491 m = x x

What we Learned 1)We learned that the meaning of the extended response is showing the work and writing the steps used in solving the problem. 2)The angle of depression is the angle formed by the horizontal and the line of sight to a tower position.

Credits Thank you Mr. John, Ms. Visico, Ms Lewis And Mr. Dawaliby for helping us to do this project. We would also like to thank our Group members: Happy, Imtashal, Christian and Angelo for taking a role in completing the math project.

Tower of Depression By Mehnaz Noreen Nancy Paucar Hui Jun Zhuo Doreen Mao

Problem A fire warden’s tower 43 m tall the angle of depression from the window of the tower to a fire in the woods is 50. How far away from the base of the tower is the fire? (Use the extend response in solving the problem. )

Tower of Depression 1. Draw and label the shape 2. Use a calculator to find the decimal of tangent 850 3. Cross multiply 4. Estimate the solution to the nearest meter

How to solve Tan 850 = x43 11. 43005 (43) = x X 491 m 90 -5=85 50 850 43 m Fire wood x

What we need to know We need to understand what the problem is asking n Know what trigonometry ratio to use n Know how to use the calculator to find Tangent 850 n Know the steps n Know how to draw the shape and label it n

What we have learned We have learned to work as a group. n We also learned to help each other. n We learned to use Tangent and work with problems involving depression n

Credit We give thanks to Mr. John for giving us the opportunity to do this project and for supporting us. We also thank Ms. Lewis for showing us how to use the computer. We recognize the work of all the group members for completing this project. Thanks to Mehnaz Noreen for being a great leader. We also thank Ms. Visico for also helping us in some parts of our project. Thanks to Nancy Paucar, Hui Jun Zhuo, and Doreen Mao for their work and support.

Trigonometric Functions and the Angle of Elevation Yuan G. Xue Qin Z. Idanelly F. Manuel Q

The Problem l A Pershing student observes the angle of elevation from a point 25 ft from the base of a tree on level ground to the top of the tree is 300. What is the altitude of the tree expressed to the nearest foot? We’ll solve this problem using an extended response.

What do you need to know What is the formula for the tangent ratio? l How to use the calculator for calculating tangent? l What kind of trigonometric ratio to use? l

Process Draw and label the right triangle. l Use the calculator to determine tangent 300. l Set up the equation. l Cross multiply. l Round the solution to the nearest foot. l

Solve Tangent 300 = O/A 0. 57735/1 = X/25 25(0. 57735) = X 14. 3375 = X 14 feet = X x 300 25 ft

What have we learned How to use a calculator to determine the tangent ratio l How to set up an equation and solve for x l How to use technology in solving trigonometric function l

The Credits We want to thank Mr. John, Ms. Visico and Ms. Lewis for letting us do this project. We also thank our group members Yuan, Xue Qin, Idanelly, Manuel for working together and seeing the project to its completion.