February 7th copyright2009merrydavidson

Happy Birthday to:

Madison Bynum 1/27

Nick Arnold 1/30

Dana Barber 2/6

Krystal Carmona 2/6

Applications of Trigonometric

Functions

Section 4-8

Example 1:A bridge is to be constructed across a small river from post Ato post B. A surveyor walks 100 feet due south of post A. Shesights on both posts from this location and finds that the anglebetween the posts is 73. Find the distance across the river frompost A to post B.

It follows that x = 327.

The distance across the river from post A to post B is 327 feet.

Post BPost A

100 ft.

x

73○10073tan

x

Word problem means word answer!

Bearings

• We use bearings to describe the direction something is traveling or the direction in which we see something.

A bearing measures the acute angle that a path or line of sight makes with a fixed north/south line.

Reading Bearings

• Many directions are given using a combination of two cardinal headings and degree number

• North (N) and South (S) are always first• Then the number of degrees• Finally the East (E) or West (W) heading

• Example: N 53° W

W

N

E

S

AB

CD

O

40º

75º

25º

20º

Reading Bearings

Bearing to A: N 70° E

Bearing to B: N 40° W

Bearing to C: S 15° W

Bearing to D: S 25° E

Example 2A boat leaves the entrance of a harbor and travels 40 miles on a bearing of S64E. How many miles south and east did the has the boat traveled?

S64E40

miles

4064cos

a a

ba64cos40

a5.17

4064sin

b

b64sin40

b3617.5 miles south, 36 miles east

Alternate Bearing Method• Problems may just give you a single bearing

• 130 degrees

• This is always referenced from North clockwise to the bearing (heading).

N

130

3) Draw a right triangle with right angle at C, angle A = 34.2 degrees,

side “b” = 19.4 mm.Solve the triangle

(solve means find all of the other sides and angles).

B = 55.80, a = 13.2 mm, c = 23.5 mm

C 34.2A

B

19.4mm

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

104.6 ft

5) 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 to of the smokestack is 530. Find the height “s” of the smokestack alone.

125.4 ft.

6) 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. Find the angle of depression of the bottom of the pool.

top of water: 20m

Pool floor

1.3m

4m

angle of depression

7.70

7) Draw a diagram that represents each bearing.

a) bearing of 320

b) bearing of 300

c) N 420 E

d) S 310 E

e) N 520 W

Homework

Section 4-8; pg 359-361

Questions 16,18,20,22,30,36,37

Draw pictures, show all work for credit!