Applications of Trig Functions

EQ: How do I use trigonometry in real-life application problems?

Angles of Elevation and Depression

1. 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

2. 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°

?

3. 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

?

4. A train must climb at a constant gradient of 5.5 m for every 200 m of

track. Find the angle of incline.

200 m5.5 m

?

Trigonometry and 3-D Figures

EQ: How do you find trigonometric ratios to find

unknown sides and angles in 3-D figures?

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

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

base diagonal.

11. Find the angle between QW and the base of the 3-D figure. Let QR =

6cm, SX = 10cm and XZ = 8cm

12. Find the angle PV makes with QV.

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

base

Areas of Triangles

EQ: How do you find the area of a triangle using

trigonometry?

Review

What happens if you don’t know the height???

There are some cases where you don’t need the height to find the

area…

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

Labeling a Triangle

If you have a triangle ABC with angles A, B, C the sides

opposite these angles are a, b, c

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

Find the area of the triangle: