Radicals, Trigonometric Ratio & Simplifying Square Roots Page 3
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Chapter Summary and Review continued
Examples on
10.3
30 -60 -90 T
RIANGLES
pp. 549–551
EXAMPLES
Find the value of each variable.
a.
b.
30
x
60
30
57
x
30
y
60
y
By the 30 -60 -90 Triangle Theorem,
By the 30 -60 -90 Triangle Theorem,
the length of the hypotenuse is twice
the length of the longer leg is the length
the length of the shorter leg, so
of the shorter leg times 3 ,
x
2(57)
114.
30
≈ 17.3.
so 30
x 3 and x
3
The length of the longer leg is the
2x ≈ 34.6.
Then y
length of the shorter leg times 3 ,
so y
57 3 .
Find the value of each variable. Write your answers in radical form or
as a decimal to the nearest tenth.
x
35.
36.
37.
38.
y
x 60
60
x
x
30
30
30 y
y
45
30 y
94 3
60
60
25
19
Examples on
10.4
T
R
ANGENT
ATIO
pp. 557–559
EXAMPLE
Find tan A and tan B as fractions and as decimals.
leg opposite to a A
2
1
A
tan A
1.05
leg adjacent to a A
2
0
29
20
leg opposite to a B
2
0
≈ 0.9524
tan B
leg adjacent to a B
B
21
C
2
1
Find tan A and tan B as fractions in simplest form and as decimals.
Round your answers to four decimal places if necessary.
39.
B
40.
41.
A
20 3
A
C
34
4 13
16
8
20
40
A
30
C
B
12
C
B
Approximate the value to four decimal places.
tan 17
tan 81
tan 36
tan 24
42.
43.
44.
45.
578
Chapter 10 Right Triangles and Trigonometry
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