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WARM UP

1)Find the altitude a

1)Find the missing legs.

3) m<1 = 2x + 4 and the m<2= 2x+10.

a)Find x if <1 and <2 are complementary

b) if they are supplementary

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Unit 6-Lesson 2

Right Triangle

Trigonometry• I can name the sides of right triangle in relation

to an acute angle.

• I can solve for an unknown side of a right triangle using sine, cosine, and tangent.

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• Remember: Trigonometry – the study of the relationships between the sides and angles of triangles

• Trigonometric ratio – a comparison of the lengths of two sides of a right triangle

In right triangles :

• The segment across from the right angle ( ) is labeled the hypotenuse “Hyp.”.

• The “angle of perspective” determines how to label the sides.• Segment opposite from the Angle of Perspective( ) is labeled “Opp.”• Segment adjacent to (next to) the Angle of Perspective ( ) is labeled

“Adj.”.

* The angle of Perspective is never the right angle.

AC

AB

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A

B C

Hyp.Angle of PerspectiveOpp.

Adj.

BC

Labeling sides depends on the Angle of Perspective

A

AC Hyp

BC Opp

AB Adj

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A

B C

Angle of Perspective Hyp.

Opp.

Adj.

If is the Angle of Perspective then ……

*”Opp.” means segment opposite from Angle of Perspective

“Adj.” means segment adjacent from Angle of Perspective

If the Angle of Perspective is

AC Hyp

AB Opp

BC Adj

C

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A

AC Hyp

BC Opp

AB Adj

thenA

B C

Opp

Hyp

Adj

thenA

B C

Opp

Adj

Hyp

Trigonometry Ratios

If is the Angle of Perspective then …...

Sin =

Cos =

tan =

C

C

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A

B C

Angle of Perspective

Opp

Hyp

C Adj

Hyp

C Opp

Adj

OppHyp

Adj

• There is one way used to help remember these ratios:

SOHCAHTOA

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sinecosine

tangent

O – opposite

A – adjacent

H - hypotenuse

Opposite over hypotenuse

Example: Find the value of x.

Step 1: Mark the “Angle of Perspective”.

Step 2: Label the sides (Hyp / Opp / Adj).

Step 3: Select a trigonometry ratio (sin/ cos / tan).

Sin =

Step 4: Substitute the values into the equation.

Sin 25 =

Step 5: Solve the equation : Change Sin 25 into a decimal (MAKE SURE CALCULATOR IS IN DEGREE MODE). Cross multiply and solve.

Opp

Hyp

9

12

x

x12 cm

25

A

B C

Angle of Perspective

Hypopp

Adj

12

x0.4226

1x = (0.4226) (12)

x = 5.07 cm=

Solving Trigonometric Equations

There are only three possibilities for the placement of the variable ‘x”.

X Opp

Hyp

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Sin = Sin = x

HypSin = Opp

x

x12 cm

25

A

B C

x12 cm

25

A

B C

25 cm

x

12 cm

A

B C

We will learn about this tomorrow!!!

Sin 25 =

12

x

1x = (12) (0.4226)

x = 5.04 cm

0.4226 = 12

x

Sin 25 = 12

x

0.4226 = 12

x1

x = 12

0.4226

x = 28.4 cm

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1. Find sin A.

A.

B.

C.

D.

2. Find sin B.

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3. Find cos A.

A.

B.

C.

D.

4. Find cos B.

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5. Find tan A.

A.

B.

C.

D.

6. Find tan B.

Find x. Round to the nearest hundredth if necessary.

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C

7 x

36°A B

OppositeAdjacent

Hypotenuse

Find x. Round to the nearest hundredth if necessary.

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C

12

x63°

A B

OppositeAdjacent

Hypotenuse

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EXERCISING A fitness trainer sets the incline on a treadmill to 7°. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor?

Let y be the height of the treadmill from the floor in inches. The length of the treadmill is 5 feet, or 60 inches.

Answer: The treadmill is about 7.3 inches high.

Multiply each side by 60.

Use a calculator to find y.

KEYSTROKES: 60 7 7.312160604ENTERSIN

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A. 1 in.

B. 11 in.

C. 16 in.

D. 15 in.

CONSTRUCTION The bottom of a handicap ramp is 15 feet from the entrance of a building. If the angle of the ramp is about 4.8°, about how high does the ramp rise off the ground to the nearest inch?