Applications and Models

Objective: To solve a variety of problems using a right triangle.

Example 1

• Solve the right triangle for all missing sides and angles.

Example 1

• Solve the right triangle for all missing sides and angles.• The angles of the triangle need to add to 1800. 1800 – 900 – 34.20 = 55.80

Example 1

• Solve the right triangle for all missing sides and angles.

4.192.34tan 0 a

a

a

18.13

2.34tan4.19 0

08.55

Example 1

• Solve the right triangle for all missing sides and angles.

4.192.34tan 0 a

c

4.192.34cos 0

a

a

18.13

2.34tan4.19 0

02.34cos

4.19c

46.23c

08.55

You Try

• Solve the right triangle for all missing sides and angles.

You Try

• Solve the right triangle for all missing sides and angles.• The missing angle is 0000 622890180

You Try

• Solve the right triangle for all missing sides and angles.

b

4028tan 0 028tan

40b

23.75b

062

You Try

• Solve the right triangle for all missing sides and angles.

b

4028tan 0

c

4028sin 0

028tan

40b

028sin

40c

20.85c

23.75b062

Example 2

• A safety regulation states that the maximum angle of elevation for a rescue ladder is 720. A fire department’s longest ladder is 110 feet. What is the maximum safe rescue height?

Example 2

• A safety regulation states that the maximum angle of elevation for a rescue ladder is 720. A fire department’s longest ladder is 110 feet. What is the maximum safe rescue height?

• We need to solve for a.

a072sin110

11072sin 0 a

a6.104

Example 3

• At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 350, whereas the angle of elevation to the top is 530. Find the height s of the smokestack alone.

Example 3

• At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 350, whereas the angle of elevation to the top is 530. Find the height s of the smokestack alone.

• First, we find the height to the top of the smokestack.

20053tan 0 sa

sa 053tan200

sa 41.265

Example 3

• At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 350, whereas the angle of elevation to the top is 530. Find the height s of the smokestack alone.

• Next, we find the height of the building.

20035tan 0 a

a035tan200

a04.140

Example 3

• At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 350, whereas the angle of elevation to the top is 530. Find the height s of the smokestack alone.

• We subtract the two values to find the height of the smokestack.

37.12504.14041.265

Example 4

• A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool is slanted so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep end, as shown. Find the angle of depression of the bottom of the pool.

Example 4

• A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool is slanted so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep end, as shown. Find the angle of depression of the bottom of the pool.

20

7.2tan

20

7.2tan 1

69.7

Trig and Bearings

• In surveying and navigation, directions are generally given in terms of bearings. A bearing measures the acute angle that a path or line of sight makes with a fixed north-south line. Look at the following examples.

Trig and Bearings

• In surveying and navigation, directions are generally given in terms of bearings. A bearing measures the acute angle that a path or line of sight makes with a fixed north-south line. Look at the following examples.

Trig and Bearings

• You try. Draw a bearing of:

W200N E300S

Trig and Bearings

• You try. Draw a bearing of:

W200N E300S

020030

Class work

• Pages 521-522

• 2-8 even

Homework

• Pages 521-522

• 1-7 odd

• 15-21 odd

• 27, 29, 31