#### Apply the Tangent Ratio

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Transcript Apply the Tangent Ratio

5.2 Apply the Tangent Ratio
p. 157
Vocabulary
Trigonometry: branch of mathematics that
deals with the relationships between the
sides and angles of triangles and the
calculations based on these relationships
Trigonometric ratio: ratio of lengths of 2
sides in a right triangle
B
C
A
Vocabulary
OPPOSITE – Across from
HYPOTENUSE – Side across from Rt Angle
ADJACENT – Next to (not the Hypotenuse)
B
C
A
3 Trig Ratios…
Tangent (TAN) – ratio of the length of the opposite
side to the length of the leg adjacent to the angle.
We’ll learn about Sine (SIN) and Cosine (COS) in
Section 5.3
Here’s how we remember it…
SOH
CAH
B
TOA
C
A
TANGENT (TAN)
tan A
leg OppositeA BC
leg Adjacent A AC
B
C
A
EXAMPLE 1
Find tangent ratios
Find tan S and tan R. Write each answer as a fraction
and as a decimal rounded to four places.
SOLUTION
tan S = opp S = RT = 80
ST
18
adj. to S
= 40
9
4.4444
tan R = opp R = ST = 18
RT
80
adj. to R
= 9
40
= 0.2250
GUIDED PRACTICE
for Example 1
Find tan J. Round to four decimal places.
ANSWER
0.7500
ANSWER
0.5333
EXAMPLE 2
ALGEBRA
Find a leg length
Find the value of x.
SOLUTION
x
32
24 ft
EXAMPLE 2
ALGEBRA
Find a leg length
Find the value of x.
SOLUTION
25
32
x
CLASSWORK
p. 159 #’s 1-6, 11-13
EXAMPLE 3
Estimate height using tangent
LAMPPOST
Find the height h of the lamppost to the nearest inch.
opp.
tan 70o =
adj.
h
40
tan 70o =
40 tan 70
o
109.9
Write ratio for
tangent of 70o.
Substitute.
= h
h
Multiply each
side by 40.
Use a calculator to
simplify.
ANSWER
The lamppost is about 110 inches tall.