Warm%20Up

1
Warm Up 1. What is the third angle measure in a
triangle with angles measuring 65 and
43? Find each value. Round trigonometric ratios
to the nearest hundredth and angle measures to
the nearest degree. 2. sin 73 3. cos 18 4.
tan 82 5. sin-1 (0.34) 6. cos-1 (0.63) 7.
tan-1 (2.75)
72
0.96
0.95
7.12
20
51
70
2
8-5
Law of Sines and Law of Cosines
Holt Geometry
3
Example 1 Finding Trigonometric Ratios for
Obtuse Angles
Use your calculator to find each trigonometric
ratio. Round to the nearest hundredth.
A. tan 103
B. cos 165
C. sin 93
tan 103 ? 4.33
cos 165 ? 0.97
sin 93 ? 1.00
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8.5 Practice (On a Separate Sheet of Paper)
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You can use the Law of Sines to solve a triangle
if you are given two angle measures and any
side length (ASA or AAS) or two side lengths
and a non-included angle measure (SSA).
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Example 2A Using the Law of Sines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
FG
Law of Sines
Substitute the given values.
Cross Products Property
FG sin 39 40 sin 32
Divide both sides by sin 39?.
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Example 2B Using the Law of Sines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
m?Q
Law of Sines
Substitute the given values.
Multiply both sides by 6.
Use the inverse sine function to find m?Q.
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8.5 Practice (Continued)
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The Law of Sines cannot be used to solve every
triangle. If you know two side lengths and the
included angle measure or if you know all three
side lengths, you cannot use the Law of Sines.
Instead, you can apply the Law of Cosines.
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Example 3A Using the Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
XZ
XZ2 XY2 YZ2 2(XY)(YZ)cos Y
Law of Cosines
Substitute the given values.
352 302 2(35)(30)cos 110
XZ2 ? 2843.2423
Simplify.
Find the square root of both sides.
XZ ? 53.3
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Example 3B Using the Law of Cosines
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
m?T
RS2 RT2 ST2 2(RT)(ST)cos T
Law of Cosines
Substitute the given values.
72 132 112 2(13)(11)cos T
49 290 286 cosT
Simplify.
Subtract 290 both sides.
241 286 cosT
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Check It Out! Example 3d
Find the measure. Round lengths to the nearest
tenth and angle measures to the nearest degree.
m?R
PQ2 PR2 RQ2 2(PR)(RQ)cos R
Law of Cosines
Substitute the given values.
9.62 5.92 10.52 2(5.9)(10.5)cos R
92.16 145.06 123.9cosR
Simplify.
Subtract 145.06 both sides.
52.9 123.9 cosR
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8.5 Practice (Continued)
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Lesson Quiz Part I
Use a calculator to find each trigonometric
ratio. Round to the nearest hundredth. 1. tan
154 2. cos 124 3. sin 162
0.49
0.56
0.31
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Lesson Quiz Part II
Use ?ABC for Items 46. Round lengths to the
nearest tenth and angle measures to the nearest
degree. 4. m?B 20, m?C 31 and b
210. Find a. 5. a 16, b 10, and m?C 110.
Find c. 6. a 20, b 15, and c 8.3. Find
m?A.
477.2
21.6
115
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Lesson Quiz Part III
7. An observer in tower A sees a fire 1554 ft
away at an angle of depression of 28. To the
nearest foot, how far is the fire from an
observer in tower B? To the nearest degree, what
is the angle of depression to the fire from tower
B?
1212 ft 37