math 9

1. Math 9
Trigonometric Ratios of Special Angles
45-45-90 degrees Right
Triangle Theorem
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2. Review
- Define an isosceles triangle.
• An isosceles triangle is a triangle with
(at least) two equal sides.
- What are the properties of an
isosceles triangle?
• two sides are equal.
• two angles are equal.

3. Yakan fabrics.

4. Yakan fabrics.

5. M9GE –Ivb–c-1
Trigonometric ratios
of special angles
- Illustrate 45∘ - 45∘ -90∘
right triangle theorem
- Find the missing length of a
45∘ - 45∘ -90∘ Right Triangle.
Objectives

6. A 45 45 90 triangle is a special type of
isosceles right triangle where the two
legs are congruent to one another and
the non-right angles are both equal to
45 degrees.
Concept

7. 45 – 45 – 90 Triangle Theorem
In a 45∘ – 45∘ – 90∘ triangle;
Concept
the legs are congruent.
the length of the hypotenuse is
2 times the length of a leg.
∴ hypotenuse = 2 leg

8. Concept and Skills
Example # 1. Find the value of x.
x x
20cm
45∘

9. Concept and Skills
Example # 2. Find the value of c.
4ft
c
45∘

10. Tanya, who is 5ft tall, is
flying a kite on 100ft of
string. How high is the kite
from the ground?

11. Practice makes perfect!
If your answers is not an integer,
express it in simplest radical form.
Find the value of each variable
used in the figure.

12. Practice makes perfect!
Rubrics Points
Criteria 5 3 1
Content Complete and
correct answers
Complete but
incorrect
answers
Incomplete and
incorrect
answers
Presentation Very Accurate Partially Accurate Inaccurate
Teamwork 80% and above
participated
50% and above
participated
Below 50%
participated
Time
Management
Finished before
the time
Finish within the
time
Not able to
finished

13. Quiz
Fig. A Fig. B Fig. C
45∘
45∘
45∘
5
5
t
x
x
30m
6ft
y
x
1. Refer to fig. A. What is the value of t?
For numbers 2-3, refer to fig. B.
2. What is the value of x?
3. If the hypotenuse is equal to 20m,
what is the value of x?
For numbers 4-5, refer to fig. C.
4. What is the value of x?
5. What is the value of y?
𝑎. 8 b. 10 c. 12 d. 6
𝑎. 10 2 b. (15 2 )/2
c. 15 2
𝑎. 5 2 b. 10 2 c. 15 2 𝑑. 10
𝑎. 6𝑓𝑡 b. 6 2 ft c. 2 d. 3
d. (30 2 )/3

14. Assignment
Let triangle ABC be a 45 -45 -90
degrees triangle where angle C = 90
degrees. Find AB if;
1. AC = 3 2. BC = 5