“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 - 460

III. 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 Expectation

B. 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 : √2

Leg 1 : Leg 2 : Hypotenuse = n : n : n√2

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:

a2+b2=c2

12 + 12 =c2

1 + 1 =c2

2 = c2

√2 = c

Example 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 : √2

4(1) : 4(1) : 4(√2)

4 : 4 : 4√2

4√2 = 5.656854249 = 5.66

Answer: The length of the hypotenuse is 4√2 or 5.66 meters.

Example 2:

Solution:

x = y

Hypotenuse = 14

Hypotenuse = x(√2)

14 = x(√2)

14/√2 = x

(14/√2) * √2/√2 = x

7√2 = x

7√2 = 9.899494937 = 9.9

Answer:

x = 7√2

y = 7√2

b. 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 : √3 : 2.

Leg 1 : Leg 2 : Hypotenuse = n : n√3 : 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.

1

Through Pythagorean Theorem:

a2+b2=c2

12 + b2 = 22

1 + b2 = 4

b2 = 4 – 1

b2=3

b = √3

Example: Find the length of the hypotenuse of a right triangle if the lengths of the other

two sides are 5 inches and 5√3 meters.

Solution: 1 : √3 : 2

5(1) : 5(√3) : 5(2)

5 : 5√3 : 10

Answer: The length of the hypotenuse is 10 meters.

Example 2:

Solution:

x(√3) = 2

x = 2/√3

x = (2/√3) * √3/√3

x = (2√3)/3 = 1.154700538 = 1.15

y = 2x

y = 2[(2√3)/3]

y = (4√3)/3 = 2.309401077 = 2.31

Answer:

x = (2√3)/3

y = (4√3)/3

C. 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)/3 y = (10√3)/3 2. a = 45° A = 4√2 B = 4√23. x = 4√3 y = 8√3