1. -- How to solve right triangles
Trigonometry
-- How to solve right triangles

2. Agenda Attention Vocabulary Sum of the Angles in a Triangle
Pythagorean Theorem
Tangent
Sine
Cosine
Applying the Trigonometric Ratios

3. Hypotenuse
Legs
Right Angle

4. Attention Trigonometry only happens in right triangle.
The ratio of any two sides remains constant even if the triangle is enlarged or reduced. (Similar triangles) B3
26 cm B2
29 cm
35 cm B1
25 cm
37 cm
14 cm A C3 C2 C1

5. Vocabulary

6. Angle of inclination：the acute angle between the horizontal and a line or line segment
Angle of elevation: the angle between the horizontal through eye level and a line of sight to a point above eye level
Angle of depression: the angle between the horizontal through eye level and a line of sight to a point below eye level
Indirect measurement: a measurement made using a ratio, formula, or other mathematical reasoning
Angle of depression
Angle of inclination
Angle of elevation

7. Sum of the Angles in a Triangle
In any triangle, the sum of the measures of the three angles is always equal to 180º B
100°
42°
38° A C

8. Pythagorean Theorem
In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (legs). A c b B C a

9. Example
10 cm
6 cm X

10. Tangent(tan) A c
Adjacent b B C a
Opposite

11. Example 1 Determine the Tangent Rations for AnglesX 12 Y Z 6

12. Example 2 Using the Tangent Ratio to Determine the Measure of AngleH 5 4 G J

13. Example 3 Using the Tangent to Determine an Angle of Inclination
The latitude of Fort Smith, NWT, is approximately 60 °. Determine whether this design for a solar panel is the best for Fort Smith. Justify your answer. A
Solar panel
9ft C
12ft B

14. Solution
Solar panel A
9ft C
12ft B

15. Sine(sin) and Cosine(cos)
hypotenuse A c
Adjacent b C B a
Opposite

16. Example 1 Determine the Sine and Cosine of an AngleE
12cm
5cm D F
13cm

17. Example 2 Using the Tangent Ratio to Determine the Measure of Angle8 K M 3 N

18. Example 3 Using Sine or Cosine to Solve a Problem
A water bomber is flying at an altitude of 5000ft. The plane’s radar shows that it is 8000ft from the target site. What is the angle of elevation of the plane measured from the target site, to the nearest degree? A
8000ft
5000ft X R

19. Solution A
8000ft
5000ft R X

20. Applying
3A ladder is 6.5m long. It leans against a wall. The base of the ladder is 1.2m from the wall. What is the angle of inclination of the ladder to the nearest tenth of a degree?

21. From the top of a 20-m high building , a surveyor measured the angle of elevation of the top of another building and the angle of depression of the base of that building. The surveyor sketched this plan of her measurements. Determine the height of the taller building to the nearest tenth of a meter.

22. More
Nowadays we are learning the function,let us see the consine function and the sine function.
2018/6/9