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 OppositeA 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.