Trigonometric functions are used to solve real-world problems involving angles of elevation, depression, and inclination. Examples include finding the angle of depression from a security camera to a door, calculating the length of an escalator given its angle of elevation and vertical rise, and determining the height of a flagpole based on the length of its shadow and the sun's angle. Trigonometry can also be applied to find unknown sides and angles in three-dimensional figures, as well as to calculate the area of a triangle when only two sides and the included angle are known.

1. Applications of Trig
Functions
EQ: How do I use trigonometry
in real-life application problems?

2. Angles of Elevation and
Depression

6. 4. A closed circuit television camera is
mounted on a wall 7.4 feet above a security
desk in an office building. It is used to view
an entrance door 9.3 feet from the desk.
Find the angle of depression from the
camera lens to the entrance door.
7.4 feet
?
?
9.3 feet

7. 5. The world’s longest escalator is the
Leningrad Underground in Lenin Square. The
escalator has an angle of elevation of 10.36°
and a vertical rise of 195.8 ft. Find the
length of the escalator.
195.8 feet
10.36°
?

8. 6. Find the height of a flagpole which
casts a shadow of 9.32 m when the sun
makes and angle of 63 to the horizontal.
9.32 m
63
63
?

9. 7. A train must climb at a constant
gradient of 5.5 m for every 200 m of
track. Find the angle of incline.
5.5 m
?

10. 8. Find , the pitch of the roof.

14. Trigonometry and 3-D
Figures
EQ: How do you find
trigonometric ratios to find
unknown sides and angles in 3-D
figures?

15. 9. In the triangular prism, find DF and
the angle AFD.

16. 10. All edges of a square-based pyramid
are 10 cm in length. Find the angle
between the slant edge and a base
diagonal.

17. 11. Find the angle between QW and the
base of the 3-D figure.

18. 12. Find the angle PV makes with QV.

19. 13. A symmetric square-based pyramid
has base lengths of 6cm and height of
8cm as shown. Find the measure of the
face TQR and the base

20. Areas of Triangles
EQ: How do you find the area of
a triangle using trigonometry?

21. Review

22. What happens if you don’t
know the height???
There are some cases where you don’t
need the height to find the area…

23. What happens if you don’t
know the height???
There are some cases where you don’t
need the height to find the area…
You have two sides and the
included angle

24. Labeling a Triangle
If you have a triangle ABC with
angles A, B, C the sides opposite
these angles are a, b, c

25. Formula for the Area of a Triangle
when you have 2 sides and the included
angle.
The area of triangle is half of the
product of two sides and the sine of
the included angle

26. Find the area of the triangle: