# 第二學習階段

```Key Stage 3
Measures, Shape and Space Dimension
Learning Unit: Trigonometric Ratios and Using Trigonometry
Learning Objectives:
•
understand the sine, cosine and tangent ratios for angles
between 0 to 90
• explore the properties and relations of trigonometric ratios
• apply trigonometric ratios to find measures of 2-D figures
Programme Title: Trigonometric Ratios
Programme Objectives
1. Introduce three common trigonometric ratios: sine ratio, cosine ratio,
tangent ratio.
2. Use graphical method to find the values of trigonometric ratios of different
angles and explore the relation between the sizes of the angles and the
values of their trigonometric ratios.
3. Apply trigonometric ratios of angles to solve daily life problems.
Programme Content
In preparing for his lessons, a mathematics teacher explains the idea of
trigonometry and introduces the application of trigonometric ratios to solve a
simple surveying problem.
The programme points out that a trigonometric ratio is the ratio of the length of
any two sides of a right-angled triangle. The changes of the values of the
trigonometric ratios with the sizes of the respective angles are explored with the
help of a unit circle on a coordinate plane.
-1-
The applications of trigonometric ratios in daily life examples are illustrated:
angle of inclination of a slope, vertical height of a slope from the ground, area
of a farm land.
1.
sin = 3/5,  ≈ 36.87, cos  ≈ 0.8；
length of adjacent side = 4, cos  = 0.8.
2. AD = 240 cos35, CD = 240 sin35,
BCD = 60, BD = CD tan60 = 240 sin35 tan60;
AB = 240 cos35 + 240 sin35 tan60 ≈ 435.03(km).
3.
= 20,
= 70;
= 32.8920 = 12.89;
length of the height of the trapezium = 12.89 tan70,
area of trapezium ≈ 936.55m2,
area of farm land ≈ 1133.40m2
-2-
Key Stage 3 ETV Programme
《Trigonometric Ratios》
Worksheet
1. In the diagram, find the value of cos .
Method 1 Calculate the value of .
5
3
=
5
3
≈

cos  ≈
Method 2 Calculate the length of the adjacent side.
Length of adjacent side of  =
cos  =
2. Location B is north of location A. A plane flew from A to B. At first, it flew
in a direction of 35 away from the direct route. After flying for 240 km, it
turned through an angle of 65 in order to reach the destination. Calculate
the distance between A and B.
Ｂ
Draw the height, CD, of ABC.
65
Ｄ
C
In BDC, calculate BCD and BD：
240 km
35
Ａ
-3-
 distance between A and B =
3. Is it true that the area of the farm land in the programme is 1100 m2?
In the programme, the area of the triangle is worked out as 196.85 m2.
Now, let’s calculate the area of the trapezium:
Size of the angle marked with
=
Size of the angle marked with
=
Length of the adjacent side of
=
Length of the height of the trapezium：
Area of the trapezium：
 the area of the farm land =
-4-
```
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