# 9-Trigonometric Ratios

```Solving Proportions Worksheet
Name: ______________________
Date: _________ Section: ______
Each problem could be set up this way:
1. Write the proportion.
8 = 192
3
n
8 · n = 192 · 3
8n = 576
8n = 576
8
8
n = 72
2. Write the cross products
3. Multiply
4. Undo multiplication by using
division
5. Divide
Solve each proportion. Be sure to set it up the correct way and show all work.
1. 4 = 10
9
x
2. 5 = x
2 6
3. 5 = 2
2 x
4. 21 = x
27 18
5. 15 = 20
21
y
6. b = 39
26
9
7. h = 0.435
108
8. 4.56 = 70
w
10. 350 = 0.25
p
11.
g
1134
= 0.95
9. 0.65 = j
15
12. 1.75 =
z
104
The Right Triangle Trigonometric Ratios – Although we won’t prove this fact until a future geometry
course, all right triangles that have a common acute angle are similar. Thus, the ratios of their
corresponding sides are equal. A very long time ago, these ratios were given names. These
trigonometric ratios (trig ratios) will be introduced through the following exercises, each of which refer
to the diagram below.
C
3
B
In a right triangle:
tangent of an angle =
sine of an angle =
leg opposite of the angle
leg opposite of the angle
hypotenuse
cosine of an angle =
hypotenuse
5
A
4
Exercise #3: tan A =
tan C =
Exercise #4: sin A =
sin C =
Exercise #5: cos A =
cos C =
A Helpful Mnemonic For Remembering the Ratios:
SOH-CAH-TOA
Sine is Opposite over Hypotenuse – Cosine is Adjacent over Hypotenuse – Tangent is Opposite over
Exercise #3: Find each of the following ratios for the right triangle shown below.
(a) sin A =
(b) tan B =
B
13
(c) cos A =
(d) tan A =
5
C
(e) cos B =
(f) sin B =
Algebra 1, Unit #8 – Right Triangle Trigonometry – L3
The Arlington Algebra Project, LaGrangeville, NY 12540
12
A
Name: ____________________________________
Date: ______________
Similar Right Triangles - Introduction to Trigonometry
Algebra 1 Homework
Skills
For problems 1 – 6, use the triangle to the right to find the given trigonometric ratios.
1. cos N =
N
15
2. sin N =
9
3. tan N =
M
P
12
4. sin P =
5. cos P =
6. tan P =
7. Given the right triangle shown, which of the following represents the value of tan A ?
(1)
25
24
(3)
7
24
A
(2)
24
7
(4)
24
25
7
B
8. In the right triangle below, cos Q = ?
(1)
(2)
12
5
(3)
5
12
(4)
12
17
12
13
Algebra 1, Unit #8 – Right Triangle Trigonometry – L3
The Arlington Algebra Project, LaGrangeville, NY 12540
25
24
C
12
Q
S
5
R
Kuta Software - Infinite Geometry
Name___________________________________
Trigonometric Ratios
Date________________ Period____
Find the value of each trigonometric ratio.
1) tan Z
2) cos C
X
A
35
21
34
Z
30
Y
28
C
3) sin C
B
16
4) tan X
A
35
C
Z
40
28
X
B
21
5) cos A
32
Y
24
6) sin A
30
A
B
32
C
B
16
24
34
40
C
A
7) sin Z
8) sin C
Z
B
48
14
32
Y
40
24
A
X
9) cos Z
10) tan C
Z
24
Y
C
50
C
30
18
36
X
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B
-1-
45
27
A
Worksheet by Kuta Software LLC
Find the value of each trigonometric ratio to the nearest ten-thousandth.
11) cos Z
12) cos C
Y
12
Z
B
36
9
A
X
15
13) tan C
45
C
29
A
14) tan A
50
A
27
C
C
30
40
20
21
B
B
15) tan C
16) tan X
A
Y
37
40
12
B
35
C
X
17) sin Z
Z
30
Z
50
18) sin Z
35
Y
50
X
Z
12
37
30
X
40
Y
19) sin 48°
20) sin 38°
21) cos 61°
22) cos 51°
Critical thinking questions:
23) Can the sine of an angle ever equal 2?
Why or why not?
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1
3
Find cos x.
24) sin x =
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Geometry
Name___________________________________
Solving Right Triangles
Date________________ Period____
Find the missing side. Round to the nearest tenth.
1)
2)
x
6
72°
73°
6
x
3)
4)
x
x
24°
37°
12
12
5)
6)
x
14
49°
14
51°
x
7)
8)
x
16
15°
x
16
63°
©n a2A0r1X2w ZKmurtHab gSFoGfWtawjaJrmeb OLQLnCl.k I TA0lylC Zrbi8gYhptnso VrMeTskelrcvieKdm.I a TMJajdTeI xwFiytvhQ mI9nSfdinnIi6tYeU hGHe9oSmeeGtkrSy6.Q
-1-
Worksheet by Kuta Software LLC
9)
10)
29
x
x
21
68°
55°
11)
12)
x
21°
x
22
29
19°
13)
14)
29
35
33°
45°
x
x
15)
16)
47°
28
34
x
59°
x
Critical thinking question:
17) Write a new problem that is similar to the
others on this worksheet. Solve the
question you wrote.
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-2-
Worksheet by Kuta Software LLC
Name: ____________________________________
Date: __________________
Using Trigonometry to Solve for Missing Sides
Algebra 1 Homework
Skill
In problems 1 through 3, determine the trigonometric ratio needed to solve for the missing side and
then use this ratio to find the missing side.
1. In right triangle ABC, m∠A = 58 and AB = 8 . Find the length of each of the following. Round your
C
(a) BC
(b) AC
A
58
8
B
2. In right triangle ABC, m∠B = 44  and AB = 15 . Find the length of each of the following. Round
(a) AC
B
44 
15
(b) BC
C
A
3. In right triangle ABC, m∠C = 32  and AB = 24 . Find the length of each of the following. Round
B
(a) AC
24
32
(b) BC
Algebra 1, Unit #8 – Right Triangle Trigonometry – L5
The Arlington Algebra Project, LaGrangeville, NY 12540
C

A
4. Which of the following would give the length of hypotenuse PR in the diagram below?
(1) 8 cos ( 24 )
(2)
8
cos ( 24 )
(3) 8 tan ( 24 )
(4)
8
tan ( 24 )
R
24
Q
8
P
Applications
5. An isosceles triangle has legs of length 16 and base angles that measure 48°. Find the height of the
isosceles triangle to the nearest tenth. Hint – Create a right triangle by drawing the height.
16
16
48°
48°
6. Carlos walked 10 miles at an angle of 20 north of due east. To the nearest tenth of a mile, how far
east, x, is Carlos from his starting point?
N
10 miles
20
E
x
7. Students are trying to determine the height of the flagpole at Arlington High. They have measured
out a horizontal distance of 40 feet from the flagpole and site the top of it at an angle of elevation of
52  . What is the height, h, of the flagpole? Round your answer to the nearest tenth of a foot.
h
52 
Algebra 1, Unit #8 – Right Triangle Trigonometry – L5
The Arlington Algebra Project, LaGrangeville, NY 12540
40 ft
```
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