Lesson 26 - 29

Lesson 26

p. 2 - 11

Graph a circle from its equation.

Write the equation of a circle from its graph.

Lessons 26-29

​Instructional videos are included. Feel free to start this extra-long Quizizz before we start the unit on Trigonometry.

How Far Apart?

Distance
From here to there

TikTok - Make Your Day

You can open this webpage in a new tab.

Copy link

Open in new tab

​x

​y

​r

Poll

My understanding of the Standard Equation of a Circle is best shown by this emoji.

• 😁

• 🙂

• 🙄

• 😮

SAT Connection

Multiple Choice

What is the center of the circle with equation x² + y² = 1?

• (1, 1)
• (0, 0)
• not enough information
• (-1, -1)

Multiple Choice

Is the point (3 , 5) inside, outside or on the circle with equation x² + y² = 9?

• Inside the Circle
• Outside the Circle
• On the Circle

Multiple Choice

What is the correct graph for the equation x²+y²=4?

• Answer is in none of the given

Lesson 27

p. 2 - 11

Solve Proportions

Remember the Pythagorean Theorem

Identify parts of a right triangle

Circles

Treat the
radicals like
variables.

Remember:
you can only
combine like
terms

​Get out some paper. Copy the problems. Simplify.

​The video is 12 minutes long.
Watch some.
Watch ALL.
Watch what you need to understand.
You will also learn about cube roots if you attend to the whole video.

Home

Open in new tab

Copy link

​The video is 12 minutes long.
Watch some.
Watch ALL.
Watch what you need to understand.
You will also learn about cube roots if you attend to the whole video.

Multiple Choice

Is this triangle labeled correctly?

• yes

• no

• good question

Multiple Choice

What is the length of the adjacent side?

• 8

• 15

• 17

Multiple Choice

What is the length of the side adjacent to ∠X?

• 7
• 24
• 25

Multiple Choice

What is the length of the side adjacent to ∠C?

• 30
• 40
• 50

Multiple Choice

What is the length of the side opposite ∠A?

• 30
• 40
• 50

Multiple Choice

What is the length of the side opposite ∠Z?

• 16
• 30
• 34

Multiple Choice

What is the length of the hypotenuse?

• 16
• 30
• 34

Multiple Choice

What is the length of the side opposite ∠X?

• 16
• 30
• 34

Multiple Choice

What is the equation for this circle?

• $$(x+2)+(y+2)=9$$

• $$x^2+y^2=9$$

• $$x+y=9$$

Match

Match the following

• $$R$$

• $$\overline{UY}$$

• $$Arc\ QRN$$

• $$\angle MPQ$$

• $$\overline{QR}$$

Point of Tangency

Secant

Semi Circle

Central Angle

Chord

• Point of Tangency

• Secant

• Semi Circle

• Central Angle

• Chord

Multiple Choice

The fixed point is called the ______ of the circle.

• Diameter

• Point

• Center

• Radius

Match

Match the following

• $$\overline{LQ}$$

• $$\overline{WY}$$

• $$\angle NQR$$

• $$X$$

Tangent

Chord

Inscribed Angle

Center

Major Arc

• Tangent

• Chord

• Inscribed Angle

• Center

• Major Arc

Multiple Choice

Write the standard equation of the circle with the given center and radius; center (0, 0) and radius of 9.

• $$x+y=3$$

• $$x^2+y^2=81$$

• $$x^2+y^2=9$$

• $$x^2+y^2=3$$

Multiple Choice

What is the radius of the circle with equation x² + y² = 1?

• 0
• 0.5
• 1
• 2

Multiple Choice

What is the center of the circle with equation x² + y² = 1?

• (1, 1)
• (0, 0)
• not enough information

SAT Connection

Work

p. 2 - 11

Lesson 28 p. 12 - 26

Define and calculate the sine, cosine, and tangent ratio.

The circle is a top
view of a solid
shape. What solid
could it be?

Calculate the area
of the circle.

Calculate the
circumference of the
circle.

AC is the diameter
of the circle. What
is the measure of
the angle ABC?

Multiple Choice

Does this picture show the diameter or radius of a circle?

• Diameter
• Radius

Multiple Choice

Does this picture show the diameter or radius of a circle?

• Diameter
• Radius

Lesson

Directions p. 12
28

Work

p. 12 - 26

Lesson 28.1 p. 29-30

Use sine ratio.

Multiple Choice

"θ" is used to represent an unknown ____________.

• angle

• side

• hypotenuse

Multiple Choice

What is the length of the side opposite ∠X?

• 16
• 30
• 34

Multiple Choice

$$\sin\theta=$$  

• $$\frac{opposite}{hypotenuse}$$  

• $$\frac{hypotenuse}{opposite}$$  

• $$\frac{adjacent}{hypotenuse}$$  

• $$\frac{opposite}{adjacent}$$  

Multiple Choice

• 21/35
• 28/21
• 35/28
• 28/35

Multiple Choice

Write sin Ɵ as a fraction for the triangle

• 10/15

• 15/10

• 1/5

• 5/1

Multiple Choice

What is the length of the hypotenuse?

• 16
• 30
• 34

Multiple Choice

What is the length of the side adjacent to ∠Z?

• 16
• 30
• 34

Multiple Choice

Which side is the hypotenuse?

• 1
• 2
• 3

Match

Match the following according to their meaning.

• hypotenuse

• adjacent

• opposite

• x

• $$\theta$$

longest side, opposite of right angle

the side next too

the side across from

a variable

Theta, represents angles

• longest side, opposite of right angle

• the side next too

• the side across from

• a variable

• Theta, represents angles

Find all missing measurements.

Draw

Label

the reference angle

the Hypotenuse

the Adjacent Leg and

the Opposite Leg

Draw

Label

the reference angle

the Hypotenuse

the Adjacent Leg and

the Opposite Leg

Find the missing measurements.

Find the missing measurements.

Find the missing measurements.

Work

p. 29-30

Lesson 28.2 p. 31-35

Use cosine ratio.

Use the digits 1 to 9 at most one time each, to fill in the
blanks to create a right triangle from the vertex (2,3).

2, 3

Multiple Choice

• 
  

  $$\frac{5}{13}$$
  

• $$\frac{5}{12}$$

• $$\frac{12}{13}$$

• $$\frac{12}{5}$$

Multiple Choice

• 
  

  $$\frac{3}{4}$$
  

• $$\frac{3}{5}$$

• $$\frac{4}{3}$$

• $$\frac{4}{5}$$

Multiple Choice

• 
  

  $$\frac{12}{5}$$
  

• $$\frac{5}{12}$$

• $$\frac{12}{13}$$

• $$\frac{13}{5}$$

Multiple Choice

If you are given the opposite side and hypotenuse, which trig function should you use?

• sine
• cosine
• tangent
• cotangent

Multiple Choice

If you are given the hypotenuse and an adjacent side, which trig function should you use?

• sine
• cosine
• tangent
• cotangent

Multiple Choice

The ratio of the length of the side opposite of the angle to the length of the hypotenuse is the _____________

• Sine

• Cosine

• Tangent

Multiple Choice

What is the green side labelled as using the starred angle as a starting point?

• adjacent

• opposite

• hypotenuse

Labeling

Label the sides of the triangle for Cos $$\angle$$ A​ ​

Drag labels to their correct position on the image

adjacent

opposite

hypotenuse

hypothalamus

Multiple Choice

What is the length of the hypotenuse?

• 9

• 40

• 41

• 81

Find the measurement of y.

Find all missing measurements.

x

x

Find the missing measurements.

Find the missing measurements.

x

Find the missing measurements.

x

Work

p. 31-35

Lesson 28.3 p. 36-39

Use tangent ratio.

Compare sine, cosine, and tangent ratios.

Multiple Choice

What side does x represent?

• hypotenuse
• right angle
• adjacent
• opposite

Multiple Choice

What is the length of the hypotenuse?

• 50
• 48
• 14

Multiple Choice

What is the length of the side opposite of angle C?

• 50
• 14
• 48

Multiple Choice

What is the length of the side adjacent to angle C?

• 14
• 50
• 48

Multiple Choice

Which ratio would you use to solve for x?

• Sine

• Cosine

• Tangent

Multiple Choice

Which ratio would you use to solve for x?

• Sine

• Cosine

• Tangent

Math Response

Find tan J. Writ the answer as a fraction in simplest form.

Type answer here

Correct Answer: \frac{3}{4}

Deg^°

Rad

Math Response

Find tan B. Write as a fraction in simplest form.

Type answer here

Correct Answer: \frac{12}{35}

Deg^°

Rad

Match

Match the following ratios:

• $$\frac{opposite}{adjacent}$$

• $$\frac{opposite}{hypotenuse}$$

• $$\frac{adjacent}{hypotenuse}$$

Tangent

Sine

Cosine

• Tangent

• Sine

• Cosine

Multiple Choice

Find the length of the missing side. 

• 17 cm
• 22 cm
• 15 cm
• 13 cm

Multiple Choice

The Pythagorean Theorem ONLY works on which triangle? 

• obtuse
• scalene
• isosceles
• right

Multiple Choice

Tangent is the ratio of the...

• ...the opposite side to the adjacent side for a given angle measurement.

• ...the adjacent side to the opposite side for a given angle measurement.

• ...the adjacent side to the hypotenuse for a given angle measurement.

• ...the opposite side to the hypotenuse for a given angle measurement.

Multiple Choice

tan (45) ≈

• 0.839

• 1

• 1.192

• 1.428

Find the missing measurements.

Find the missing measurements.

The tallest masonry building in
the world is City Hall in
Philadelphia (as of April 2019). If
you’re standing on the street
1,300 feet from the bottom of the
building, you have to look up at a
23 degree angle to see the top.
How tall is the building? Explain
or show your reasoning.

Work

p. 36-39

Lesson 28.4 p. 39-44

Use sine, cosine, and tangent ratios.

Gateway Arch in St. Louis, Missouri, is 630
feet tall. Priya can look up at a 50 degree
angle to see the top of the arch.

How far away from the base of the arch is
she standing?

Work

p. 39-44

Lesson 29 p. 45-47

Use trigonometric ratios to solve problems.

Read the problem.
Draw a diagram.
Solve the problem.

Find a reason
why each
one does not
belong.

Scientific Calculator Exercise
desmos.com/scientific

Mai is visiting Paris to see the
Eiffel Tower. She is 80 feet away
when she spots it. To see the top,
she has to look up at an angle of
85.7degrees.

How tall is the Eiffel Tower?

An airplane travels 150 miles horizontally
during a decrease of 35,000 feet
vertically.

1.What is the angle of descent?

2.How long is the plane's path?

The sun is 62 degrees
above the horizon. A tree
casts a shadow that is 12
feet long. How tall is the
tree?

Ramps in a parking garage need
to be both steep and safe. The
maximum safe incline for a ramp
is 8.5 degrees.

Is this a safe ramp?

Explain or show your reasoning.

SAT Connection

In this triangle, AC
bisects angle BAD.
Find AC. (Figure is
not drawn to scale.)

SAT Connection

If a circle has the
equation

what is the shortest
straight-line distance
from the center of the
circle to the origin?