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The word trigonometry means “triangle measurement.” You can use trigonometry to calculate the lengths of sides and the measures of angles in triangles.

physics

surveyingTrigonometry has been used for centuries in the study of:

astronomy geography

engineering

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A

B

Cadjacent

hypotenuse

opposite

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A

B

C

adjacent

opposite

hypotenuse

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A

B

C

opposite

adjacent

hypotenuse

oppsin

hypA

adjcos

hypA

opptan

adjA

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A

B

Copposite

adjacenthypotenuse

oppsin

hypB

adjcos

hypB

opptan

adjB

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A

B

C

opp

adj

hyp

SOH CAH TOA

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A

B

C

8

6

10opp

adj

hyp

SOHCAHTOA

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A

B

C

5

12

13

adj

opp

hyp

SOHCAHTOA

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A

B

C

Example 1: Determine side b

55º

b

8 cm

b =

b =

tan8

Bb

tan 558

b

opp

adj

SOHCAHTOA

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A

B

C

Example 2: Determine side c if A is 31°.

hyp

adj

SOHCAHTOA

13 cm

c

1331cos

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P

Q

R

17 cm

Example 3: Determine side p if P is 45°.

opposite

hypotenuseSOHCAHTOA

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Ex. 4: From a distance of 20 m from the base a lighthouse the angle of elevation to the top of a lighthouse is 38º. Determine the height of the lighthouse.

38º

h

The lighthouse is m high.

20 m

h

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Workbook pg.5 #1-3, 5, 6, 9, 10, 13