Transcript LENGTH OF LEG OPPOSITE B - Evergreen Education Organization

“Success in math is considered a
gateway to many educational
and occupational opportunities”.
(Jetter, 1993)
GRANT UNION HIGH SCHOOL
•
Title I school
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2,000 – 2,200 student population
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90% of students have free lunch (low social economic
status)
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40% of student population are English Language
Learners (Hispanic; Hmong and Lao refugees)are Special
Education
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At least 30% of students don’t live with parents (foster
home, relatives)
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Math skills of at least 50% of student population is 1 to
2 grade levels behind
COLLABORATION GOALS
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70% of students in each class achieve in math
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Weekly collaboration to discuss lesson delivery, teaching
strategies, assessment results, and make revisions to
plans as needed
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Standards-driven reform is the primary approach
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Activate student conceptual knowledge when presented
with a real-life problem solving situation
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Improve student motivation, participation, and
generalization skills of students
TEACHER COLLABORATION
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Involves teachers of same subject matter
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Weekly collaboration to discuss lesson delivery, teaching
strategies, assessment results, and make revisions to
plans as needed
•
Standards-driven reform is the primary approach
•
Planning for curriculum, pacing, common formative
assessments, sharing of best practices during summer
break
TRIGONOMETRY
三角法
GREEK WORD MEANING:
在希腊的词汇中就是指：
TRIANGLE
MEASURE
三角形计算
IN 140 B.C.
HIPPARCHUS
BEGAN TO USE
AND WRITE
TRIGONOMETRY
在公元前140年希帕庫斯
（Hipparchus）就已经开始使
用三角法并撰写相关著作了。
ANCIENT
GREEKS USED
TRIGONOMETRY
TO MEASURE
THE DISTANCE
TO THE STARS
古希腊人曾使用三角法计算地
球到恒星的距离。
OBJECTIVES:
1. TO FIND TRIGOMETRIC RATIOS OF A RIGHT
TRIANGLE.
2. TO FIND VALUES OF TRIGOMETRIC FUNCTIONS.
3. TO APPLY THE TRIGOMETRIC FUNCTIONS TO
SOLVE RIGHT -TRIANGLE PROBLEMS.
•WE WILL DEAL ONLY WITH RIGHT
TRIANGLES
我们将只对直角三角形进行说明
90
RIGHT TRIANGLES MUST HAVE A 90 DEGREE ANGLE
直角三角形必须有一个90度的角。
HYPOTENUSE
斜边
LEG OPPOSITE TO B
角B的对边
LEG ADJACENT TO
ANGLE B 角B的邻边
B
HYPOTENUSE
LEG OPPOSITE
TO B
B
LEG ADJACENT TO B
SINE OF B = LENGTH OF LEG OPPOSITE B
LENGTH OF HYPOTENUSE
COSINE OF B = LENGTH OF LEG ADJACENT TO B
LENGTH OF HYPOTENUSE
TANGENT OF B = LENGTH OF LEG OPPOSITE B
LENGTH OF LEG ADJACENT TO B
斜边
角B的对边
B
角B的邻边
sinB =角B对边长/斜边长
cosB = 角B邻边长/斜边长
tanB = 角B对边长/角B邻边长
SAMPLE RIGHT TRIANGLE PROBLEMS
直角三角形例子
1.)
x
20
c
b
z
30
Ø
a
y
Find the values to the nearest tenth of:
b/c
A.) sin Ø = _______
A.) XY = ________
11.5
a/c
B.) cos Ø = _______
23.1
B.) YZ = ________
b/a
C.) tan Ø = _______
60
APPLICATIONS:
To avoid a steep descent, a
plane flying at 30,000 ft. starts
its descent 130 miles away
from the airport. For the angle
of descent Ø, to be constant, at
what angle should the plane
descend?
应用：
一个飞机在30,000英尺的高
空飞行，为避免急剧下降，
要从离机场130英里的时候开
始降落。下降时与地面的角
度 Ø一定, 求Ø?
tan Ø = 30,000
5,280*130
Ø
30,000 ft.
Ø
130 Miles
An observer 5.2 km from a launch
pad observes a rocket ascending.
A. At a particular time the angle of elevation is 37
degrees. How high is the rocket?
B. How far is the observer from the rocket?
C. What will the angle of elevation be when the
rocket reaches 30 km?
b
37
A. Tan 37 = a_
5.2
B. Cos 37 = 5.2
b
C. Tan Ø = 30
5.2
5.2
a
一个观测员在离发射台5.2 km的
地方观测火箭升空。
A. 在某一时刻，仰角是37度，这时火箭离地面多
高？
B. 这一时刻观测员离火箭多远？
C. 当火箭到达 30 km 高空时，仰角是多少？
A ship sails 340 kilometers on a bearing of 75
degrees.
A. How far north of its original position is the ship?
B. How far east of its original position is the ship?
一只船朝东北方向75度航行了340km.
A. 这只船距原来位置的北方多远？
B. 这只船距原来位置的东方多远？
b
A. Cos 75 = a
340
B. Sin 75 =
b
340
a
340
75
BY THE STUDY OF TRIGONOMETRY---------YOU TOO COULD REACH FOR THE STARS!!!!!!!!!!!
BE A ROCKET!!!!!!!
REACH FOR THE STARS!
BY THE STUDY OF TRIGONOMETRY---------YOU TOO COULD REACH FOR THE STARS!!!!!!!!!!!
BE A ROCKET!!!!!!!
REACH FOR THE STARS!
APPLICATION ACTIVITY
TRIGONOMETRY PROJECT
with CLINOMETER WORKSHET