9.3 Trigonometry Part I

9.3 TRIG RATIOS AND SIDES

WARM UP

Florida’s B.E.S.T. Standards for
Mathematics

MA.912.T.1.1
Define trigonometric ratios for
acute angles in right triangles.

MA.912.T.1.2
Solve mathematical and real-
world problems involving right
triangles using trigonometric
ratios and the Pythagorean
Theorem.

MA.K12.MTR.2.1
Demonstrate understanding by
representing problems in multiple ways.

MA.K12.MTR.4.1
Engage in discussions that reflect on the
mathematical thinking of self and others.

MA.K12.MTR.5.1
Use patterns and structure to help
understand and connect mathematical
concepts.

Florida’s Mathematical
Thinking and Reasoning
Standards

USE THE 3 SIMILAR TRIANGLES ON THE
LEFT AND FIND THE PROPORTION OF

SMALL LEG TO BIG LEG.
𝟔
𝟏𝟕 = . 𝟑𝟓𝟐𝟗

=

=

What do we observe?

FIRST, WE NEED TO NAME THE

SIDES OF THE TRIANGLE.

1)Mark your reference

angle (x or 𝜃)

2)Mark your hypotenuse

(H)

3)Mark the adjacent

side(A) and the
opposite side (O)
________

________

________

________

LABELING TRIANGLES

• Angle x

• Angle C

D

S

N

​Angle N

Multiple Choice

Which side is opposite angle x?

• 1
• 2
• 3

Multiple Choice

Where would you label 'h'?

• Opposite the given angle.

• Opposite the right angle.

• The unknown side.

• The side that has a length already given.

Multiple Choice

Where would you label 'o'?

• Opposite the given angle.

• Opposite the right angle.

• The unknown side.

• The side that has a length already given.

Multiple Choice

Which side is adjacent to angle x?

• 1
• 2
• 3

THREE TRIGONOMETRIC RATIOS:

Sin(𝒙°):

𝑶𝒑𝒑𝒐𝒔𝒊𝒕𝒆

𝑯𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆

Cos(𝒙°):

𝑨𝒅𝒋𝒂𝒄𝒆𝒏𝒕

𝑯𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆

Tan(𝒙°):

𝑶𝒑𝒑𝒐𝒔𝒊𝒕𝒆
𝑨𝒅𝒋𝒂𝒄𝒆𝒏𝒕

𝑶𝒑𝒑𝒐𝒔𝒊𝒕𝒆

𝑨𝒅𝒋𝒂𝒄𝒆𝒏𝒕

𝑨𝒅𝒋𝒂𝒄𝒆𝒏𝒕

𝑶𝒑𝒑𝒐𝒔𝒊𝒕𝒆

SOH CAH TOA
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WE DO:

Trig Function

∠𝑨

∠𝑩

Sine (Sin)

Cosine (Cos)

Tangent (Tan)

WRITING
TRIG
RATIOS

Multiple Choice

What is the trigonometric ratio for sin(Z)?

• 32/40

• 24/40

• 32/24

• 24/32

Multiple Choice

What is the trigonometric ratio for tan(A)?

• 21/29

• 20/29

• 21/20

• 20/21

Multiple Choice

What is the trigonometric ratio for cos(Z)?

• 9/15

• 12/15

• 9/12

• 12/9

Multiple Choice

What is the trigonometric ratio of sin(C)?

• 14/50

• 48/50

• 14/48

• 48/14

WE DO:

How do we use Trig Ratios?

1. Identify and Label what you have.

2. Write an equation and solve for the variable.

3. Use your calculator to solve.

Work and Answer:

YOU DO:

How do we use Trig Ratios?

1. Identify and Label what you have.

2. Write an equation and solve for the variable.

3. Use your calculator to solve.

Work and Answer:

Draw

Draw the labels on this triangle:

H for hypotenuse

O for opposite

A for adjacent

Draw

Draw the labels on the triangle.

H for hypotenuse

O for opposite

A for adjacent

Draw

Draw the labels on the triangle.

H for hypotenuse

O for opposite

A for adjacent

Draw

Draw the labels on the triangle.

H for hypotenuse

O for opposite

A for adjacent

Poll

How confident do you feel about this content?

• Not at all confident -

  I feel lost

• Somewhat confident -

  I think I'm getting it

• Pretty confident - I just need a bit more practice but I get it

• Very confident - Give me the test now! I got this!

Multiple Choice

Choose the correct ratio.

• cos(33)=x/14
• sin(33)=x/14
• cos(33)=14/x
• sin(33)=14/x

Multiple Choice

Find the measurement of the missing side indicated

• 4.98
• 5.98
• 3.20
• 4.18

Multiple Choice

Solve for x. Round to the nearest tenth.

• 9.8
• 0.1
• 0.038
• 9.9

Multiple Choice

Solve for x. Round to the nearest tenth.

• 5.7

• 5.1

• 9.6

• 4.1

Multiple Choice

Solve for x. Round to the nearest tenth.

• 24.2

• 21.0

• 27.8

• 36.8

Multiple Choice

What equation can be used to solve for x?

• Sin(40°)= x/40 
• Sin(40º)=x/19
• Cos(40º)=x/19
• Tan(40°)=19/x

Multiple Choice

Solve for x. Round to the nearest tenth.

• 9.9

• 5.4

• 22.6

• 4.8

Multiple Choice

To solve for the missing angle, what trig equation do we set up?

• $$x=\sin^{-1}\left(\frac{300}{400}\right)$$

• $$x=\cos^{-1}\left(\frac{300}{400}\right)$$

• $$x=\tan^{-1}\left(\frac{300}{400}\right)$$

• $$x=\tan^{-1}\left(\frac{400}{300}\right)$$

Multiple Choice

Solve for the missing angle

• 32°
• 44°
• 61°
• 50°

Multiple Choice

Which expression is correct for "y"?

• y = tan^–1(31/23)

• y = sin^–1(31/23)

• y = cos^–1(31/23)

Multiple Choice

Find the measure of the indicated angle (?) round to the nearest tenth.

• 9.4
• 55.2
• 20.15
• 19.4

Multiple Choice

Solve for x. Round to the nearest tenth.

• 23.6

• 5.1

• 10.0

• 17.3

Multiple Choice

You are standing at A, looking up at the airplane. It is 400 m horizontally in front of you and 300 m high.  What is the angle of elevation to the airplane as shown in the diagram? 

• $$37\degree$$

• $$38\degree$$  

• $$51\degree$$

• $$49\degree$$

Multiple Choice

Find the value of each variable.

• $$x=11\sqrt{3}$$  and  $$y=22$$  

• $$x=22$$  and  $$y=22$$  
  

• $$x=22\sqrt{3}$$  and  $$y=22$$  
  

• $$x=11$$  and  $$y=22$$  
  

Multiple Choice

The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach?

• 12 feet

• 13.9 feet

• 169 feet

• 18 feet