“Special Right Triangles”I. Objectives/Focus Skills At the end of the lesson, the students are expected to: 1. identify the two types of special right triangles. 2. explain how the ratio in solving special right triangles are obtained. 3. show the ability to solve special right triangles. 4. follow the instruction in solving.II. Subject Matter Special right triangles Two types of special right triangles Solving special right triangles Material: Instructional material References Internet Source: http://www.onlinemathlearning.com/index.html http://www.basic-mathematics.com/special-right-triangles.html www.wikipedia.com Book: Stewart, J. , Redlin, L. & Watson, S. (2010). Algebra and Trigonometry Second Edition, pp. 459 - 460III. Procedure 1. Opening prayer. 2. Greetings. 3. Have a game related to math. 4. Identify what are special right triangles. 5. Identify the two types of special right triangle.
6. Explain how the ratios in special right triangles are obtained. 7. Show how to solve each special right triangle through a ratio. 8. Give an evaluation and assignment. 9. Closing prayer.A. Motivation 1. Intrinsic Motivation a. Challenge student through a game. b. Use instructional material. 2. Extrinsic Motivation a. Praise b. High ExpectationB. Lesson Proper/Teaching – Learning Activities Content SPECIAL RIGHT TRIANGLES A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. a. 45° - 45° - 90° triangle It is a special right triangle whose angles are 45°, 45° and 90°. It is also called an isosceles right triangle. The lengths of the side are in the ratio of 1 : 1 : Leg 1 : Leg 2 : Hypotenuse = n : n : n
The triangle has 45° on two of its angles and it is an isosceles triangle which means that its two sides are equal. Through Pythagorean Theorem: 12 + 1 2 = 1 + 1 = 2= =cExample 1: Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are both 4 meters.Solution: 1 : 1 : 4(1) : 4(1) : 4( ) 4:4:4 4 = 5.656854249 = 5.66Answer: The length of the hypotenuse is 4 or 5.66 meters.
Example 2: Solution: x=y Hypotenuse = 14 Hypotenuse = x( ) 14 = x( ) 14/ =x (14/ )* =x 7 =x 7 = 9.899494937 = 9.9 Answer: x=7 y=7b. 30° - 60° - 90° triangle It is a special right triangle whose angles are 30°, 60° and 90°. The lengths of the sides are in the ratio of 1 : : 2. Leg 1 : Leg 2 : Hypotenuse = n : n : 2n
In an equilateral triangle, we can obtain the ratio. Let say that “a” is equal to 2. We divided the triangle into two equal parts and we get the 30° -60° - 90° triangle. 1Through Pythagorean Theorem: 12 + = 22 1 + = 4 =4–1 b =
Example: Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are 5 inches and 5 meters. Solution: 1 : :2 5(1) : 5( ) : 5(2) 5:5 : 10 Answer: The length of the hypotenuse is 10 meters. Example 2: Solution: x( )=2 x = 2/ x = (2/ )* / x = (2 )/3 = 1.154700538 = 1.15 y = 2x y = 2[(2 )/3] y = (4 )/3 = 2.309401077 = 2.31 Answer: x = (2 )/3 y = (4 )/3C. Values Statements/ Generalizations Special right triangles give us a better and easier way of computing its sides which can be very useful in our application to life.
D. Evaluation Solve the triangle. 1. 2. 3.IV. Assignment/Agreement Review and study the lesson discussed.
Lesson Plan“Special Right Triangles” Submitted by: Eileen M. Pagaduan Nalla Anncy L. Rosarda JC Bell M. Torres BSE 22 Submitted to: Mr. Iryl Marc Pantoja
Key to correction:1. x = (5 )/3 y = (10 )/32. a = 45° A = 4 B=43. x = 4 y=8