Transcript Examples 2-3

EXAMPLE 2
Find cosine ratios
Find cos U and cos W. Write each answer as a
fraction and as a decimal.
SOLUTION
cos U = adj. to U
hyp
=
UV =
UW
18 =
30
3
5
0.6000
cos W = adj. to W =
hyp
WV =
UW
24 =
30
4
5
0.8000
EXAMPLE 3
Use a trigonometric ratio to find a hypotenuse
DOG RUN
You want to string cable to make a dog run from two
corners of a building, as shown in the diagram. Write
and solve a proportion using a trigonometric ratio to
approximate the length of cable you will need.
EXAMPLE 3
Use a trigonometric ratio to find a hypotenuse
SOLUTION
sin 35o =
opp
hyp
sin 35o =
11
x
Substitute.
x sin 35o =
11
Multiply each side by x.
x =
x
x
11.
sin 35o
11.
0.5736
19.2
Write ratio for sine of 35o.
Divide each side by tan. 35o
Use a calculator to find tan. 35o
Simplify.
ANSWER
You will need a little more than 19 feet of cable.
GUIDED PRACTICE
for Examples 2, and 3
In Exercises 3 and 4, find cos R and cos S. Write each
answer as a decimal. Round to four decimal places, if
necessary.
SOLUTION
Find SR, use the Pythagorean Theorem
ST2 + TR2 = SR2
122 + 92 = SR2
15 = SR
R
cos R = adj. to
=
hyp
RT
SR
=
9
15
=
3
5
0.6
cos S = adj. to S =
hyp
ST
SR
=
12
15
=
4
5
0.8
GUIDED PRACTICE
for Examples 2, and 3
In Exercises 3 and 4, find cos R and cos S. Write each
answer as a decimal. Round to four decimal places, if
necessary.
SOLUTION
Find SR, use the Pythagorean Theorem
ST2 + TR2 = SR2
162 + 302 = SR2
34 = SR
R
cos R = adj. to
=
hyp
RT
SR
=
30
34
0.8824
cos S = adj. to S =
hyp
ST
SR
=
16
34
0.4706
GUIDED PRACTICE
for Examples 2, and 3
In Example 3, use the cosine ratio to find the
length of the other leg of the triangle formed.
5.
SOLUTION
cos35o =
o
cos 35 =
19.2 cos35o =
adj
hyp
x
19.2
x
x = 15.7
Write ratio for cosine of 35o.
Substitute.
multiply each side by 19.2
Simplify.