11-20-2025JASA Trig Ratios, Missing Sides, Missing Angles

​Agenda
Mood Meter
Bell Ringer
Trig Ratio CFU
Trig for missing sides
Trig for missing angles
Exit Ticket

Take out your
TI-84 Calc

Take out paper for notes

Poll

Which Selena Gomez are you today?

• 1

• 2

• 3

• 4

• 5

Open Ended

You ca only have one gift card. Which one and why?

Pythagorean Theorem & Trigonometry

• I can combine trig ratios and the Pythagorean Theorem to solve for a missing side or angle in a right triangle.

• I can interpret and solve applied (word-problem) situations involving right triangles using trig and Pythagorean reasoning.

• I can verify solutions by checking consistency between trig ratio, Pythagorean Theorem, and context.
  I can explain how similarity in right triangles leads to definitions of sine, cosine, and tangent.

• I can identify opposite, adjacent, and hypotenuse sides in a right triangle for a given acute angle.

• I can compute the sine, cosine, or tangent of an acute angle in a right triangle.

• I can solve for a missing side or angle in a right triangle using trig ratios.

• I can apply right-triangle trigonometry to real-world problem contexts (e.g., heights, inclines).

Where is trigonometry used in the daily life?

* Video Game Design

* Speaker Placement in Concert Venues

* Architecture/Construction

* Criminology

* Military

Knowledge Check

Draw

Label the sides of the triangle.

Adjacent - Green

Hypotenuse - Purple

Opposite - Orange

Labelling

Label the sides of the triangle.

Drag labels to their correct position on the image

Adjacent

Hypotenuse

Opposite

Multiple Choice

Which side is adjacent to angle x?

• 1
• 2
• 3

Multiple Choice

Which side is opposite angle x?

• 1
• 2
• 3

Multiple Choice

Which side is the hypotenuse?

• 1
• 2
• 3

Math Response

 Find sin(A)

Type answer here

Correct Answer: \frac{4}{5}

Deg^°

Rad

Math Response

 Find cos(A)

Type answer here

Correct Answer: \frac{15}{17}

Deg^°

Rad

Math Response

 Find tan(X)

Type answer here

Correct Answer: \frac{4}{3}

Deg^°

Rad

​Take out paper/pencil/pen, markers for notes

Radians to Degree Mode - TI Nspire

🎯 How to Change TI-Nspire & TI-84 From Radians to Degrees

(If you see “RAD” in the top-right corner, that means your calculator is in radians.)

• Turn on the calculator.

• Press the MODE key.
• Look at the third line on the MODE screen.

• Move the cursor until it is on top of the word Degree.
• Press ENTER to select it.
• Degree should now be highlighted.

• Press 2nd then QUIT to go back to the home screen.
• Your calculator is now in Degree mode.

TI-Nspire: ​Radians to Degree Mode

TI-84: Radian to Degree Mode

STEP 1:

Label your Sides and the given angle.

*Label your reference angle with the THETA SYMBOL
* Label only the sides you need:
Opposite, Adjacent, Hypotenuse
(You can use O, A, and H for short!)

​

STEP 2:

What am I Solving For?

What is given? What is missing?

Given:

22 = theta
x = adjacent side
30 = hypotenuse

​

STEP 3:

Which trig function do I need?
sin cos tan

Given:

22 = theta
x = adjacent side (A)
30 = hypotenuse (H)

​

STEP 4:

Write the TRIG EQUATION
YOU CANNOT SKIP THIS STEP

Given:

22 = theta
x = adjacent side (A)
30 = hypotenuse (H)

​

STEP 5:

cross mutiply and solve

​

STEP 6:

cross mutiply and solve
Calculator
Time!

A. Click on the wrench in the upper right corner. Click on Degrees. SUPER IMPORTANT!

B. Click on Keyboard icon- then FUNCTIONS, then TRIG.

C. Enter trig expression.

D. Round to the nearest tenth (one decimal place).

​

TI-84: Radian to Degree Mode

STEP 7: cross mutiply and solve
27.81551563…
round to nearest ten-thousandth unless otherwise directed.
Why?
more decimal places = more accurate answer
27.81551563…
27.8155

​x = (cox 22) (30)
x = 27.8155

Draw

Draw theta on the angle

Label the given sides (not all 3 sides)

Open Ended

Write the TRIG EQUATION to solve for x.

Math Response

What is the value of x?

Round to the nearest ten-thousandth place (four digits after the decimal).

Type answer here

Correct Answer: 8.9200

Deg^°

Rad

Draw

Label the angle with theta.

Label only the sides needed to find VW

Open Ended

Write the TRIG EQUATION needed to find VW.

Math Response

What is the length of VW to the nearest tenth.

Type answer here

Correct Answer: 7.0

Deg^°

Rad

STEP 1: Label your Sides and the given angle.
STEP 2: What am I Solving For?
STEP 3: Which trig function do I need? sin cos tan
STEP 4: Write the TRIG EQUATION-YOU CANNOT SKIP THIS STEP
STEP 5: cross multiply and solve
STEP 6: cross multiply and solve Calculator Time!

STEP 7: round to instructed digit

​Remember the steps....

Steps to Success

STEP 1: Label your GIVEN Sides and reference angle.
STEP 2: What am I Solving For?
STEP 3: Which trig function do I need? sin cos tan
STEP 4: Write the TRIG EQUATION -
YOU CANNOT SKIP THIS STEP
STEP 5: Input equation into Desmos Calc or TI Nspire
STEP 6: Round to instructed digit

​Solving for a Missing Angle

Solving for a Missing Angle

​Inverse Trig Ratios

​There are two types of notation for inverse functions

REGARDLESS OF NOTATION
WE ALWAYS SAY "inverse" NEVER "arc" OR "to the -1"

• arcsin = sin^-1 we say "inverse sine" or "sine inverse."

• arccos = cos^-1 we say "inverse cosine" or "cosine inverse."

• arctan = tan^-1 we say "inverse tangent" or "tangent inverse."

Using trig. to calculate
an angle measure
EXAMPLES - Write these
down

Using trig. to calculate an angle measure
EXAMPLES - Write these down

​Write the equation by the example.

​​Write the equation next to the example.

​​Write the equation next to the example.

​Type in Calc -make sure you are in DEG Mode

​​Write the equation next to the example.

​Type in Calc -make sure you are in DEG Mode

​38.68 degrees.

​48.19 degrees.

​21.80 degrees.

​​Write the equation next to the example.

​Type in Calc -make sure you are in DEG Mode

​38.68 degrees.

​48.19 degrees.

​21.80 degrees.

​​Write the equation next to the example.

​Type in Calc -make sure you are in RAD Mode

0.68 radians

0.84 radians

​0.38 radians

​​Write the equation next to the example.

​Make sure your notes are correct!

Draw

Label the given sides outside the triangle: O, H, or A

Write the trig ratio for theta on the upper left corner.

Go to DESMOS Calculator OR use your TI 84 Calculator

https://www.desmos.com/calculator

Write the angle measure inside the triangle.

Multiple Choice

Choose the correct ratio.

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

Draw

Label the given sides outside the triangle: O, H, or A

Write the trig ratio for theta on the upper l

Go to DESMOS Calculator OR use your TI 84 Calculator https://www.desmos.com/calculator

Write the angle measure inside the triangle.

Draw

Label the given sides outside the triangle: O, H, or A

Write the trig ratio for theta on the upper left corner.

Go to DESMOS Calculator OR use your TI 84 Calculator:

https://www.desmos.com/calculator

Write the angle measure inside the triangle.

Draw

Draw theta on the angle

Label the given sides

Determine and write the Trig ratio needed

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

What is the correct equation to solve for x ?

• $$\frac{\tan46}{1}=\frac{17}{x}$$

• $$\frac{\sin46}{1}=\frac{x}{17}$$

• $$\frac{\tan46}{1}=\frac{x}{17}$$

• $$\frac{\cos46}{1}=\frac{x}{17}$$

Multiple Choice

Which is the correct set up to solve for x?

• $$\frac{\sin24}{1}=\frac{x}{12}$$

  
  

• $$\frac{\cos24}{1}=\frac{x}{12}$$

• $$\frac{\tan24}{1}=\frac{x}{12}$$

• $$\frac{\tan\ 24}{1}=\frac{12}{x}$$

Multiple Choice

Solve for x. Round to the nearest tenth.

• 103.5
• 4.7
• 55.0
• 23.4

Multiple Choice

Find x round to the nearest tenth.

• 46.1
• 4.9
• 16.4
• 26.9

Multiple Choice

What is the correct equation to solve for x ?

• $$\tan\left(46\degree\right)=\frac{17}{x}$$

• $$\sin\left(46\degree\right)=\frac{x}{17}$$

• $$\tan\left(46\degree\right)=\frac{x}{17}$$

• $$\cos\left(46\degree\right)=\frac{x}{17}$$

Multiple Choice

John is building a fence and needs to cut a piece of wood at a specific angle. If he needs to cut it to the nearest degree, what would be the measure of the angle?

• 32

• 33

• 34

• 35

​IXL Geometry

Q8: Find trigonometric functions using a calculator
Q11 Trigonometric ratios: find a side length

Q12 Trigonometric ratios: find an angle measure



Due by Sunday, 11/23/2025 5 pm

Poll

What is your level of confidence of today's lesson?

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