3a.Notes-Finding Missing Angles

Name: ___________________________________ # ___________

Example 1

Geometry: Period _____________

Ms. Pierre

Date: ______________

Let ¡Ï? and ¡Ï? be acute angles in two right triangles. Use a

calculator to approximate the measures of ¡Ï? and ¡Ï? to the

nearest tenth of a degree.

Finding Missing Angles

a.) sin A = 0.76

b.) cos B = 0.17

Today¡¯s Objective

SWBAT use trigonometric ratios for acute angles in right triangles

to find missing angles.

The ratios of the side lengths of a right triangle depend on the

measure of its acute angles. These are called _______________

__________.

Sine of ¡Ï? (sin A) =

?

=

?

?

Check for Understanding

Find ?¡Ï? to the nearest tenth of a degree if

'

(

cos T = 0.64

Cosine of ¡Ï? (cos A) =

Tangent of ¡Ï? (tan A) =

?

?

?

?

=

*

(

=

'

*

Thinking ¡°_____-_____-_____¡± can help you remember these

ratios. Using these ratios, you can find the length of any side of

a right triangle if you know one acute angle and any other side.

Find ?¡Ï? to the nearest tenth of a degree if

sin D = 0.48

4

4. sin B

Solve Right

Triangles AB

Name ¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Inverse Cosine If cos A 5 z, then

AC

21 }

cos21 ztangent,

5 m¡Ï A.

5 m¡Ï A

LESSON

Goal p Use

sine, andcos

cosine

Example

2 inverse

AB ratios.

5.4

5. cos B

6. tan B

Date ¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Practice

8

A. }

17

A

15

17

C. }

8

B. }

17

Guided Practice

17

8

15

Use

a calculator

to approximate

the measure ofwith

¡Ï? to the

} ratios

}

D.

E. }

F. of

trigonometric

correct ratio.Use

Some

VOCABULARY

a calculator to approximate

the measure

15

15

8 ¡Ï? to the

Example

1 Match

Usethe

an inverse

tangentexpression

to find an anglethe

measure

nearest tenthmay

of abe

degree.

used more than once, and some may not be used at all.

nearest tenth of a degree.

C

Solvea acalculator

right1.triangle

Use

sin to

A approximate

2. the

cos A

measure of ¡Ï A to the nearest tenth

of a degree.

16

5

55. cos B,

Because tan4.A sin

5B

21

INVERSE

TRIGONOMETRIC

5 m¡Ï A. Using aRATIOS

calculator,

tan

21

.

tan

Let ¡Ï A be an ................
................

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