Unit 9: Right Triangles and Trigonometry

Name: ________________________________________________ Date: ____________________ Block: ____________

Topic/Assignment

I CAN statement

Turned in?

Simplifying Radicals

HW: Radicals Worksheet

1) I can recognize perfect square factors

2) I can simplify radicals completely

Yes No

Pythagorean Theorem

HW: Pythagorean Theorem

Worksheet

1) I can find sides of a right triangle using Pythagorean

theorem

2) I can use the converse to determine if a triangle is a right

triangle.

Yes No

Special Right Triangles A

HW:

45 45 90

Worksheet

1) I can recognize a

45 45 90

triangle

2) I can use the

45 45 90

pattern to find missing side lengths

Yes No

Special Right Triangles B

HW:

30 60 90

Worksheet

1) I can recognize a

30 60 90

triangle

2) I can use the

30 60 90

pattern to find missing side lengths

Yes No

Mid-Unit Review and Quiz

Mid-Unit Review Sheet

Yes No

Sine, cosine, and tangent ratios

HW: Trig Worksheet

1) I can apply the sine, cosine, and tangent ratios to find

missing sides lengths

Yes No

Solving Triangles

HW: Solving Triangles Worksheet

1) I can apply the inverse trig functions to find missing angle

measurements.

2) I can solve a triangle by finding all side lengths and all angle

measurements.

Yes No

Unit 9 Review

Yes No

Unit 9 Test

Name: ________________________________________________ Date: ____________________ Block: ____________

Simplifying Radicals Review

Objectives: 1) I can recognize perfect square factors

2) I can simplify radicals completely

Simplifying

Radicals

Simplify the following radical expressions completely.

1)

50

7)

10652 

13)

5

3

2)

5 300

8)

144

9

14)

18

5

3)

18

9)

75

16

15)

7

10

4)

27

10)

3

90

16)

 

2

65

5)

60

11)

45

75

17)

 

3

27

6)

5213 

12)

3

27

18)

635 

Name: ________________________________________________ Date: ____________________ Block: ____________

THE PYTHAGOREAN THEOREM/CONVERSE

Objectives: 1) I can find sides of a right triangle using Pythagorean Theorem.

2) I can use the converse to determine if a triangle is a right triangle.

Pythagorean Theorem

Pythagorean Triple

Simplify each:

A.

)6)(3(

B.

)34)(34(

C.

2

)56(

Find the length of the missing side of the triangle. Leave answers in simplified radical form.

A. B. C.

D. E. F.

Find the area of the triangle to the nearest tenth of a meter.

B.

You place a 10 foot ladder against a wall. If the base of the ladder is three ft. from the wall, how high up the wall

does the top of the ladder reach?

Draw a sketch!

Name: ________________________________________________ Date: ____________________ Block: ____________

Pythagorean Theorem Converse:

If

222

cba 

, then ABC is

_____________.

If

222

cba 

, then ABC is

_____________.

If

222

cba 

, then ABC is

_____________.

Are the triangles obtuse, right, or acute?

a) b)

Can these side lengths form a triangle? Show why or why not.

a) 5, 4, 3 b) 5, 5, 10 c) 5, 10, 15 d) 5, 10, 10

If a triangle can be formed, classify each triangle as acute, obtuse, or right based on the following side lengths.

FIRST: show if the 3 numbers can form a triangle. IF SO: show if it’s right obtuse or acute

a) 5, 12, 13 b) 6, 5, 12 c) 7, 8, 9

CAN THE SIDE LENGTHS FORM A TRIANGLE? HOW DO YOU KNOW?

Name: ________________________________________________ Date: ____________________ Block: ____________

SPECIAL RIGHT TRIANGLES (A)

Objectives: 1) I can recognize a

45 45 90

triangle

2) I can use the

45 45 90

pattern to find missing side lengths

45 - 45 - 90 Triangle Theorem

Fill in the table with the missing side lengths of the 45-45-90 triangle. Leave all answers in simplified radical form.

Leg (x)

Hypotenuse (

2x

)

5

23

26

10

62

15

14

68

45-45-90 Rules:

When you are given the length of a LEG ________________ by

2

to get the length of the HYPOTENUSE.

When you are given the length of the HYPOTENUSE _______________ by

2

to get the length of the LEG.

x

Name: ________________________________________________ Date: ____________________ Block: ____________

Find all the missing side lengths. Leave answers in simplified radical form.

a) b)

c) d)

e) f)

45°

8

45°

6

10

45°

Name: ________________________________________________ Date: ____________________ Block: ____________

SPECIAL RIGHT TRIANGLES (B)

Objectives: 1) I can recognize a

30 60 90

triangle

2) I can use the

30 60 90

pattern to find missing side lengths

30 - 60 - 90 Triangle Theorem

Fill in the table with the missing side lengths of the 30-60-90 triangle. Leave all answers in simplified radical form.

Short Leg (x)

Long Leg (

3x

)

Hypotenuse (2x)

6

20

34

32

8

27

68

18

Find all the missing side lengths.

a. b.

c. d.

x

2x

60°

30°

10

34

6

18

Name: ________________________________________________ Date: ____________________ Block: ____________

TRIGONOMETRY

Objectives: 1) I can apply the sine, cosine, and tangent ratios to find missing sides lengths

Trigonometric Ratio: the ratio of 2 sides of a right triangle.

a number

has special name(s)

helps find a missing side or angle of a right triangle

Sine

Cosine

Tangent

S O H C A H T O A

Find the sine, cosine, and tangent of

P

.

The 2 acute angles of a right triangle each have… A

C B

A

B

C

Name: ________________________________________________ Date: ____________________ Block: ____________

Find the sine, cosine, and tangent of S for the first triangle and R of the second triangle. Express each value as a

simplified fraction.

i) ii)

S

Use your calculator to find the following trig ratios (round to the nearest tenth).

sin90

= B)

cos15

= C)

tan73

=

Solve the following for the variable (round to the nearest tenth).

sin23

15

x



B)

cos74

5

w



C)

3

tan60

y



D)

18

sin80

x



E)

10

cos12

y



F)

tan68

43

z



Use trigonometric ratios to find the value of the variables. Round to the nearest hundredth.

A) B)

C) D)

5

x

27

Name: ________________________________________________ Date: ____________________ Block: ____________

SOLVING RIGHT TRIANGLES

Objectives: 1) I can apply the inverse trig functions to find missing angle measurements.

2) I can solve a triangle by finding all side lengths and all angle measurements.

RIGHT TRIANGLES HAVE:

SOLVING A RIGHT  MEANS:

TO SOLVE, YOU MUST KNOW EITHER:

*Once you know the sine, cosine, or tangent of an acute angle, you can use a calculator to find the measure of the angle.

FOR ANY ACUTE ANGLE A:

If sin A = x, then

If cos A = y, then

If tan A = z, then

If you are finding a SIDE you use ________________________.

If you are finding an ANGLE you use ______________________.

Solve the following right triangles. Round decimals to the nearest tenth.

A. B.

C. D.

Name: ________________________________________________ Date: ____________________ Block: ____________

Applications:

1) During its approach to Earth, the space shuttle’s glide angle changes.

When the shuttle’s altitude is about 15.7 miles, its horizontal distance to the

runway is about 59 miles. What is its glide angle? Round your answer to the

nearest tenth.

When the space shuttle is 5 miles from the runway, its glide angels is about 19. Find the shuttle’s altitude at this point

in its descent. Round your answer to the nearest tenth.

2) During a flight, a hot air balloon is observed by two persons standing at points A and B as illustrated in the diagram.

The angle of elevation of point A is 28. Point A is 1.8 miles from the balloon as measure along the ground. Round

answers to the nearest tenth.

What is the height, h, of the balloon?

Point B is 2.9 miles from point A. Find the angle of elevation of point B.