Special Angles Special Angles Special Angles Special Angles Special Angles

1. Solving a
Right Triangle
Given the
Length of the
Two Legs

2. “
Objectives:
At the end of the lesson, you
will be able to:
 Illustrate the six trigonometric
ratios: sine, cosine, tangent,
cotangent, secant, and cosecant.
 Solve right triangles given the
length of both sides.
2

3. 3
Direction: Tell the appropriate trigonometric ratio
(SOH, CAH, or TOA) to be used in each missing side
of ΔGIF.
1. ̅𝐹̅̅𝐼; trigonometric ratio: __________
2. ̅𝐹̅̅𝐺̅; trigonometric ratio: __________
For numbers 3 to 5, solve for the missing parts of
ΔGIF.
3. ̅𝐹̅̅𝐼 __________
4. ̅𝐹̅̅𝐺̅ __________
5. ∠F __________
21
c =
a
RECAP
I
F
G
31
29º

4. ➜ This topic covers the fourth and
last case of solving right
triangles in which the lengths of
the two legs are given.
4

5. ➜ The right triangle above has two legs
given, ̅𝐴̅̅𝐵̅ and ̅𝐵̅̅𝐶̅. Let us put all parts of the
triangle in a table and determine the
missing parts to be solved.
➜ So, in this case, the missing parts are the
hypotenuse and the two acute angles.
5

6. 1.
EXAMPLE.
Find the missing parts of the
right triangle ΔTIE.
E
T
I
y = 10
x =15

7. Given:
x = 15- leg 1
y = 10 - leg 2
Missing Parts to Solve:
(hypotenuse, two acute
angles):
1. z =?
2. ∠T =?
3. ∠E =?
7
EXAMPLE:
E
T
I
y = 10
x =15
z

8. Since two sides of
the triangle are
already given, use
the Pythagorean
Theorem to find the
hypotenuse.
8
1. Find i.
E
T
I
y = 10
x =15
z

9. By looking at the figure,
side t is opposite ∠T, and
side e is adjacent to ∠T.
To get the measure of
∠T, use TOA (tangent-
opposite-adjacent).
9
2. Find ∠T
E
T
I
y = 10
x =15
z

10. By looking at the figure,
side e is opposite ∠E,
and side t is adjacent to
∠E. To get the measure
of ∠E, use TOA
(tangent-opposite-
adjacent).
10
2. Find ∠E
E
T
I
y = 10
x =15
z

11. 2.
EXAMPLE.
Find the missing parts of the
right triangle ΔABC.
C
A
B
e = 8
d =25
f

12. 12
Directions: Given the length of the two legs, find the length of
the hypotenuse. Round off your answers to two decimal
places.
LET’S PRACTICE!
LEG 1 LEG 2 HYPOTENUSE
1. 12 cm 6 cm
2. 10 cm 5 cm
3. 8 cm 5 cm
4. 14 cm 6 cm
5. 9 cm 15 cm

13. Direction: Solve for
the missing parts of
each right triangle.
13
KEEP PRACTICING!
A
B
C
x = 7 cm
z = 15cm
z
y

14. Direction: Solve for
the missing parts of
each right triangle.
14
X
Y
Z
a = 8
KEEP PRACTICING!
b = 5
c

15. Extra graphics
15
Change the color of gray shapes with the “Recolor image” functionality. Draw your own
feet, hands and mouths to create unique characters and have fun!

16. 16
Find more icons at slidescarnival.com/extra-
free-resources-icons-and-maps
SlidesCarnival icons are editable shapes.
This means that you can:
➜ Resize them without losing quality.
➜ Change fill color and opacity.
➜ Change line color, width and style.
Isn’t that nice? :)
Examples:

17. ✋👆👉👍👤👦👧👨👩👪💃🏃💑❤😂😉
😋😒😭👶😸🐟🍒🍔💣📌📖🔨🎃🎈🎨🏈
🏰🌏🔌🔑 and many more...
17
You can also use any emoji as an icon!
And of course it resizes without losing quality.
How? Follow Google instructions
https://twitter.com/googledocs/status/730087240156643328

18. Free templates for all your presentation needs
Ready to use,
professional and
customizable
100% free for personal
or commercial use
Blow your audience
away with attractive
visuals
For PowerPoint and
Google Slides