Name______________________________ Date_______________

Integrated Algebra A Notes/Homework Packet 7

Lesson Homework

Intro to Trigonometry HW #1

Solve for a Missing Side CW/HW #2

Review/Quiz

Solve for a Missing Angle HW #3

Review Solving for Missing Angle HW #4

Mixed Questions (Solve for Side or Angle) HW #5

Quiz

Trigonometry Word Problems HW #6

Let’s

LABEL!

INTRO to TRIGONOMETRY

This is used only for right triangles – to find a missing side or angle!

Here are a couple of ways to remember the Trig. Ratios:

“S O H C A H T O A” or

“Some Old Horse-Caught Another Horse-Taking Oats Away”

Examples: Find x to the nearest tenth.

1) 2)

3) 4)

Why is this not Pythagorean theorem? __________________________________________________

_______________________________________________________________________________________

x

A

B

C

sin x = hypotenuse

opposite

cos x = hypotenuse

adjacent

tan x = adjacent

opposite

S O H

C A H

T O A

x 3 km

65

55

55

55

20 x

62 x

10 yd 45

x 10 cm

Practice: Find x to the nearest tenth.

1) 2)

3) 4)

5) 6)

x 30’c

60

37

x

20’

x

19’

35

12 in.

x

25

6

x

40 7

x 70

Name _________________________ Date ____________

HW #1

For #1 – 4, find x to the nearest tenth.

1) 2)

3) 4)

For #5 – 8, find x to the nearest whole number.

5) 6)

7) 8)

x 2 km

68

55

45

55

10 x

60 x

21 yd 35

x

15 cm

x 25m

65

34

x

23in

x

17ft

37

14

x

20

Inverse Trigonometry – Solving for an Angle

Review: We use the following when…

a) Pythagorean Theorem: a2 + b2 = c2…when we are given two sides of a right triangle

and we want to find the missing side.

b) Trigonometry: sin, cos, tan…when we are given an angle and side of a right triangle

and we want to find a missing side.

Now we are going to use…

c) Inverse Trigonometry: sin-1, cos-1, tan-1…when we are given two sides of a right

triangle and we want to find an angle.

We will still use SH

O C H

A T A

O

Example 1: Solve for angle A to the nearest degree.

20cm

15cm

x

C

B A

Step 1: Label opposite, adjacent,

hypotenuse according to angle X.

Step 2: Setup using correct trig ratio (sin,

cos, or tan).

Step 3: Take the inverse trig function of

the fraction (using 2nd

button on calc).

Step 4: Round and label answer in

degrees.

Example 2: Solve for angle D to the nearest tenth of a degree.

Example 3: Find the angle the ladder makes with the ground to the nearest degree.

Practice: Find angle Y to the nearest degree.

6ft

14ft

x F

E

D

20ft

12ft

X

2000 km

480 km N

C

Y

TRIGONOMETRY – Finding an Angle (continued)

Find x to the nearest tenth of a degree.

1) 2)

3) 4)

5) 6)

7) 8)

11yds

8yds x

12ft

x

15ft

18

12

x 5m 4m

x

8 x

18

8in

24in

x

10’

x

8’

24”

x

12”

Name _________________________ Date ____________

HW #4

Find the missing angle in each picture to the nearest degree.

1) 2)

3) 4)

5) 6)

Review:

1) Find the following using the given set of numbers:

92, 75, 86, 64, 71, 92, 67, 60, 108, 64, 73, 80, 72, 96

Median = ______________ Range = ________________

Mode = ______________ Mean = ________________

3

9

x

9

6

x

7

x

14

7

20

16

x

x

5

4

x 15

12.5

4 km x

48

55

2 cm

x

32

8 ft

19 ft

x

13 cm

12 cm

X

X

2400 km

520 km

Name _________________________ Date ____________

HW#5

Find x to the nearest tenth.

1) 2)

3) 4)

5) 6)

6 in.

x 18 in.

Trigonometry Word Problems

1. A ladder 6 feet long leans against a wall and makes an angle of 15º with the ground.

Find to the nearest tenth of a foot how high up the wall the ladder will reach.

2. A piece of lumber leans against a wall. The top of this 40 foot piece of lumber touches

a point on the wall that is 36 feet above the ground. Find to the nearest degree the

measure of the angle that the lumber makes with the wall.

3. A building casts a shadow of 11.4 meters along level ground. The rays of the sun hit the

ground at a 52º angle. What is the height of the building (to the nearest tenth of a

meter)?

4. A 5.2 m ladder leans against a wall. The bottom of the ladder is 1.9 m from the wall.

What angle does the ladder make with the ground (to the nearest degree)?

Name_______________________________ Date_________________

HW #6

1. A kite is 33 m above the ground. The kite string makes an angle of 38° with the ground.

Assuming that the string is taut, how much string is out (to the nearest tenth)?

2. As it leans against a building, the bottom of an 8 meter ladder is 3 meters from the base

of the building. What angle must the ladder be placed with the ground (to the nearest

degree)?

3. A Boeing 747 climbs to a vertical height of 35000 feet. The plane traveled in the air a

distance of 70000 feet. At what angle must the plane continuously climb (to the nearest

degree)?

4. A carpenter needs a ladder to do repair work on a building. The base of the ladder is

11ft away from the building and forms a 62 angle with the ground. To the nearest foot,

how long must the ladder be?