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- 1. ROMEO AND JULIET AND THE LADDER quit Romeo Juliet
- 2. Introduction <ul><li>Objectives: </li></ul><ul><li>Recall the properties of an isosceles right triangle. </li></ul><ul><li>Find the hypotenuse of a 45 °-45°-90° triangle using the Pythagorean Theorem. </li></ul><ul><li>Apply the special triangles to find the missing sides of a 45°-45°-90° triangle. </li></ul><ul><li>Target group: Fourth Year Students </li></ul><ul><li>Duration/Mode: 30minutes/student-centred </li></ul><ul><li>Instructions: click on the icons in the navigation bar below to move from one section to another </li></ul>quit
- 3. <ul><li>Romeo and Juliet were </li></ul><ul><li>very much in love with each </li></ul><ul><li>other. But their parents had </li></ul><ul><li>disapproved strongly of their relationship because their clans are the best of enemies. </li></ul><ul><li>Romeo wanted very much to see the love of his life Juliet. So , he visited Juliet’s place and thought of ways on how he could see Juliet secretly . </li></ul>quit
- 4. <ul><li>He saw that there </li></ul><ul><li>was a balcony near her </li></ul><ul><li>room . The height of the balcony was 5 meters , and it was perpendicular to the ground. He also knew that it will be easier to find the length of the ladder if he will place it at 45 ° angle from the ground. </li></ul><ul><li>Why? </li></ul>
- 5. quit quit <ul><ul><li>( Choose the best reason.) </li></ul></ul><ul><ul><li> The triangle formed is equiangular so the acute angles are equal. </li></ul></ul><ul><ul><li> The triangle formed is an isosceles right so the measure of the two legs are equal and both acute angles have measures of 45 ° . </li></ul></ul><ul><ul><li> The triangle formed is a right triangle with acute angles that measures 30 ° and 60 ° . </li></ul></ul><ul><ul><li> </li></ul></ul>
- 6. Very Good ! Very Good! Very Good! Very Good!
- 7. Please try Again!
- 8. 45° 5m 45° 45° 5m So Romeo started to make the ladder that will be his easiest way to reach Juliet. ladder
- 9. <ul><li>The balcony is 5 meters high and perpendicular to the ground. If the ladder will be placed 5 meters from the base of the balcony, and form a 45° angle, how long will the ladder be? (Use the Pythagorean Theorem) </li></ul>balcony wall ground ladder 5 5 45° 90° 45° <ul><ul><li>Can you guide him to find the length of the ladder? </li></ul></ul>a² + b² = c²
- 10. How do you solve for the length of the ladder? <ul><li>1. What is the length of a leg or a? </li></ul><ul><li>2. What is the length of the other leg or b? </li></ul><ul><li>3. Use the Pythagorean Theorem to solve for the hypotenuse or c. </li></ul><ul><li>a² + b² = c² </li></ul><ul><li>( Click on the icon to do your work.) </li></ul>
- 11. The length of the ladder is 5√2 meters . ( You can tell Romeo to start making the ladder) <ul><li>Let us solve for c again . </li></ul><ul><li>1. a= 4, b =4 </li></ul><ul><li>4² + 4² = c² so 16 + 16 = c². Therefore </li></ul><ul><li>32 = c², so 4√2 = c. </li></ul><ul><li>2. a = 10, b =. 10 </li></ul><ul><li>10² + 10 ² = c² so 100 + 100 = c². Therefore </li></ul><ul><li>200 = c² so 10√2 = c. </li></ul>
- 12. What conclusion can you derive from the different examples about the length of the hypotenuse given a 45°-45°- 90° triangle? The length of the hypotenuse of a 45°- 45°- 90° triangle is the length of a leg times √3. The length of the hypotenuse of a 45°- 45°- 90° triangle is one-half of the length of a leg. The length of the hypotenuse of a 45°-45°-90 ° triangle is the length of a leg times √2.
- 13. You got it
- 14. Please try again
- 15. Complete the table Practice Exercises 10 7√2 12 2 c b a
- 16. <ul><li>Excellent! If you got a perfect score. </li></ul><ul><li>Try some more exercises if you got a score of 6. </li></ul><ul><li>Go back to the examples if you got a score of 4 and below. </li></ul>
- 17. For more readings on 45 ° -45 °- 90 ° triangle please be encouraged to look at <ul><li>http://en.wikipedia.org/wiki/Special_right_triangles </li></ul><ul><li>http://www.onlinemathlearning.com/special-right-triangles.html </li></ul>quit
- 18. Evaluation <ul><li>Send your answer to sofievelasco52@yahoo. com . </li></ul><ul><li>Complete the table: </li></ul>Your assignment will be sent to you once you have send the correct answers. 6 4√2 3/4 1/2 3 c b a
- 19. Credits <ul><li>Prepared by: </li></ul><ul><li>Mrs. Sofia S. Velasco </li></ul><ul><li>Mathematics Department </li></ul><ul><li>Quezon City High School </li></ul><ul><li>September 18, 2008 </li></ul><ul><li>Special Thanks to: </li></ul><ul><li>Mr. Philip Wong </li></ul>

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