* A rope is stretched from the top of a 12m tree to the ground
* The rope is 20m long
* Let's call the distance from the tree to the end of the rope x
* Then we have a right triangle with:
* Hypotenuse (c) = Rope length = 20m
* One leg (a) = Height of tree = 12m
* Other leg (x) = Distance from tree to end of rope
* Using the Pythagorean theorem: a^2 + b^2 = c^2
* x^2 + 12^2 = 20^2
* x^2 + 144 = 400
* x^2 = 256
* x =
Angles, Triangles of Trigonometry. Pre - Calculusjohnnavarro197
This presentation will help learners to grasp and understand trigonometry concepts such as angles, triangles. It encompasses basic fundamental topics of trigonometry.
Angles, Triangles of Trigonometry. Pre - Calculusjohnnavarro197
This presentation will help learners to grasp and understand trigonometry concepts such as angles, triangles. It encompasses basic fundamental topics of trigonometry.
Triangles What are the properties of an Isosceles Triangle.pdfChloe Cheney
Learn how types and angles of triangles differ. Discover what an isosceles triangle is and its properties with example questions through our blogs and private math tutor.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Triangles What are the properties of an Isosceles Triangle.pdfChloe Cheney
Learn how types and angles of triangles differ. Discover what an isosceles triangle is and its properties with example questions through our blogs and private math tutor.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
3. What is
Trigonomet
ry?
•a branch of
Mathematics that
deals with the
properties and
applications of
ratios associated
with angles. 01
m
word
ns
nd
hich
02
03
04
4. What is
Trigonomet
ry?
•a branch of
Mathematics that
deals with the
properties and
applications of
ratios associated
with angles. 01
•it came from
the Greek word
“trigonon”
which means
“triangle” and
“metron” which
means
“measure”.
02
03
04
5. What is
Trigonomet
ry?
•a branch of
Mathematics that
deals with the
properties and
applications of
ratios associated
with angles. 01
•it came from
the Greek word
“trigonon”
which means
“triangle” and
“metron” which
means
“measure”.
02
•literally, it
means
measurement
of triangles.
03
04
6. What is
Trigonomet
ry?
•a branch of
Mathematics that
deals with the
properties and
applications of
ratios associated
with angles. 01
•it came from
the Greek word
“trigonon”
which means
“triangle” and
“metron” which
means
“measure”.
02
•literally, it
means
measurement
of triangles.
03
•Hipparchus of
Nicaea is the
founder of
Trigonometry.
04
7. Two Types of Trigonometry
PLANE
TRIGONOMETRY-
studies the
properties of
triangle on a plane
and its two
dimensional.
8. Two Types of Trigonometry
•SPHERICAL
TRIGONOMETRY-
is concerned with
relations that
exist among the
sides and angles
of a spherical
triangle.
17. • usually denoted as (°),
symbol for degree
• it represents
1
360
of full
rotation
• it is the most common unit of
angle
D
E
G
R
E
E
it is the standard unit of angular
measure commonly denoted as
rad.
it is the central angle formed
when the subtended arc is
equivalent to the radius of a circle.
R
A
D
I
A
N
18. it is sometimes called as gon,
grade or gradian.
it is equivalent to
1
400
of a full
circle.
1 grad=
9
10
degree or 1 grad =
𝜋
200
rad.
G
R
A
D
I
A
N
M
I
N
U
T
E
is equivalent to
1
60
of a
degree (1°=60’, 1’=60”)
19. it is expressed as
equivalent to
1
60
of a
minute (1°=3600’’)
S
E
C
O
N
D
it is expressed as
mil or angular mil.
1
6400
of a circle.
M
I
L
L
I
R
A
D
I
A
N
26. PROBLEM SOLVING CONVERSION
A student averaged 45
miles per hour on a
trip. What was the
student’s speed in feet
per second?
01
A room is 10 ft by 12
ft. How many square
yards are in the
room?
02
27. PROBLEM SOLVING CONVERSION
A child is prescribed a dosage of
12 mg of a certain drug per day
and is allowed to refill his
prescription twice. If there are
60 tablets in a prescription, and
each tablet has 4 mg, how many
doses are in the 3 prescriptions
(original + 2 refills)?
03
The largest single rough
diamond ever found, the
Cullinan Diamond, weighed
3106 carats. One carat is
equivalent to the mass of 0.20
grams. What is the mass of
this diamond in milligrams?
04
37. Rectangular Coordinate System
• is a system in w/c an ordered pair of numbers is associated with a point
in plane. It is also based on perpendicular real number lines.
x-axis
(abscissa)
Point of origin
y-axis
(ordinate)
Quadrant I
(+, +)
Quadrant II
(−, +)
Quadrant III
(−, −)
Quadrant IV
(+, −)
38. Coterminal Angles
• are angles in standard position which have the same terminal side.
• two angles are coterminal if the difference between them is a multiple of
360° or 2π.
40. BOTH ARE POSITIVE
Make both angles less than or equal to 360° (the
operation to be used is subtraction)
If the two positive angles are already less than or
equal to 360°, you can now verify if they are
coterminal or not.
If the two angles have the same value, then they
are coterminal. If they don’t have the same value,
then they are not coterminal
41. BOTH ARE NEGATIVE
Make both angles less than or equal to 360° (the
operation to be used is addition)
If the two positive angles are already less than or
equal to 360°, you can now verify if they are
coterminal or not.
If the two angles have the same value, then they
are coterminal. If they don’t have the same value,
then they are not coterminal
42. ONE IS NEGATIVE & ONE IS
POSITIVE
•The positive angle is same process
with number 1.
•The negative angle is same process
with number 2.
43. Tell whether the following angles are coterminal/not
210° & 930°
180° & 405°
90° & 450°
270° & 800°
-30° & -420°
01
02
03
04
05
44. Tell whether the following angles are coterminal/not
-120° & -480°
-90° & -450°
90° & -450°
480° & -240°
-60° and 90°
06
07
08
09
10
47. TRIANGLE
•it is a plane closed figure formed by three line segments.
It has 3 angles and 3 sides. The line segments form the
sides of the triangle. The angles in a triangle are called
vertices (vertex).
Right triangle
•is a triangle where one angle measures 90°
48. 2 SPECIAL TYPES OF RIGHT TRIANGLE
1. 30° – 60° – 90° / Scalene
triangle is a triangle whose acute angles measure 30° and
60°
49. 2 SPECIAL TYPES OF RIGHT TRIANGLE
2. ISOSCELES TRIANGLE
It has 2 equal sides and an angle that is 90°. The sides are
opposite the equal angles. If the two acute angles are equal,
then these measures 45° each. (45° – 45° – 90°)
50. PROPERTIES OF RIGHT ∆’S
1. One of its angles is right angle or equal to 90°,
that’s why it is called a right triangle.
2. The two acute angles in a right triangle are always
complementary, where the sum of complementary
angles is equal to 90° or ∠𝐴 + ∠𝐵 = 90°
3. The two perpendicular sides are called legs while
the longest side is the hypotenuse. The hypotenuse
“c” is opposite the right angle.
51. PROPERTIES OF RIGHT ∆’S
4. The sides are related by the Pythagorean Theorem which states
that: the sum of the squares of the two legs of the right triangle is
equal to the square of the hypotenuse or a² + b² = c², where “a”
and “b” are the lengths of the sides/legs of the right triangle and
“c” is the length of the hypotenuse.
52. What Is The Pythagorean Theorem?
• A right triangle consists of two sides called the legs and one
side called the hypotenuse. The hypotenuse is the longest side
and is opposite the right angle. (c2 = a2 + b2)
53. Find the length of the
hypotenuse of a right triangle if
the lengths of the other two
sides are 3 inches and 4 inches.
b = 4
a = 3
c = ?
Find the length of one side of a
right triangle if the length of
the hypotenuse is 10 inches
and the length of the other side
is 9 inches.
b = ?
a = 9
c = 10
54. Mason wants to lay pavers in his
families' backyard for the summer. It
is important that he start the pavers
at a right angle. If he want the
dimensions of the patio to be 8 ft by
10 ft, what should the diagonal
measure? b = 10
a = 8
c = ?
55. A kite at the end of a 40
feet line is 10 feet behind
the runner. How high is the
kite?
b = ?
a = 10
c = 40
56. At a certain dock, a ship decided
to take its departure at about 20
miles east. After reaching that
point, it made its turn at 50 miles
north. How far is the ship from the
dock?
57. A 20-m long rope is stretched
from the top of a 12-m tree to the
ground. What is the distance
between the tree and the end of
the rope on the ground?
