Various Ratios Worksheets Page 8
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14You can find the sine and cosine of an angle by using a calculator.
→
sin 63°
63
0.891006524
SIN
→
cos 63°
63
0.4539905
COS
You can use the sine and cosine ratios to find missing lengths of sides or
angle measures in a right triangle.
2
E x a mp le s
Find the length of XY in
XYZ.
km
35
˚
You know the measure of
X and the
length of the hypotenuse. You can use
the cosine ratio.
25 km
X
Y
a
d
j
a
c
e
n
t
l
e
g
cos X
X
Z
h
y
p
o
t
e
n
u
s
e
n
cos 35°
Replace X with 35°, XY with n, and XZ with 25.
2
5
(25)(cos 35°)
n
Multiply each side by 25.
25
35
20.47880111
COS
The length of XY is about 20.5 kilometers.
3
APPLICATION
Scale Drawings
Find the angle that Toni
16.5 ft
needs to draw for her scale drawing of the
Leaning Tower of Pisa.
You know the length of the leg
Explore
opposite the angle and the length of
the hypotenuse. You can use sin A.
Plan
Substitute the known values into
177 ft
the definition of sine.
o
p
p
o
s
i
t
e
l
e
g
sin A
h
y
p
o
t
e
n
u
s
e
1
6
.
5
sin A
Solve
1
7
7
A
1
16.5
177
[SIN
]
2nd
5.348898164
Toni must draw an angle of about 5°.
Toni knows the angle in her drawing will be very narrow.
Examine
Since 5° is a very small angle, it is a reasonable answer.
8
Trigonometry
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