Applications and Models
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Transcript of Applications and Models
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