integrated algebra a · integrated algebra a notes/homework packet 7 lesson homework intro to...
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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?