Download 8-5.Revised class presentation

8-5 Law of Sines and Law of Cosines
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)
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8-5 Law of Sines and Law of Cosines
Objective
Use the Law of Sines and the Law of
Cosines to solve triangles.
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8-5 Law of Sines and Law of Cosines
Use your calculator to find each
trigonometric ratio. Round to the nearest
hundredth.
A. tan 103°
B. cos 165°
tan 103°  –4.33 cos 165°  –0.97
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C. sin 93°
sin 93°  1.00
8-5 Law of Sines and Law of Cosines
Use a calculator to find each trigonometric
ratio. Round to the nearest hundredth.
a. tan 175°
tan 175°  –0.09
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b. cos 92°
cos 92°  –0.03
c. sin 160°
sin 160°  0.34
8-5 Law of Sines and Law of Cosines
You can use the altitude of a triangle to find a
relationship between the triangle’s side lengths.
In ∆ABC, let h represent the length
of the altitude from C to
From the diagram,
,
and
By solving for h, you find that h = b sin A and h = a
sin B. So b sin A = a sin B, and
.
You can use another altitude to show that these
ratios equal
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8-5 Law of Sines and Law of Cosines
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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8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths
to the nearest tenth and angle
measures to the nearest degree.
Holt Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to
the nearest tenth and angle measures
to the nearest degree.
Holt Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to
the nearest tenth and angle measures
to the nearest degree.
Holt Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths
to the nearest tenth and angle
measures to the nearest degree.
Holt Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round
lengths to the nearest tenth and
angle measures to the nearest
degree.
Holt Geometry
8-5 Law of Sines and Law of Cosines
You can use the Law of Cosines to solve a
triangle if you are given
• two side lengths and the included angle
measure (SAS) or
• three
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Geometry side lengths (SSS).
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths
to the nearest tenth and angle
measures to the nearest degree.
XZ
Holt Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to
the nearest tenth and angle
measures to the nearest degree.
mT
Holt Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to
the nearest tenth and angle
measures to the nearest degree.
DE
Holt Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to
the nearest tenth and angle
measures to the nearest degree.
mK
Holt Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to
the nearest tenth and angle
measures to the nearest degree.
YZ
Holt Geometry
8-5 Law of Sines and Law of Cosines
Find the measure. Round lengths to
the nearest tenth and angle
measures to the nearest degree.
mR
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8-5 Law of Sines and Law of Cosines
Use a calculator to find each
trigonometric ratio. Round to the
nearest hundredth.
1. tan 154°
2. cos 124°
3. sin 162°
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8-5 ΔABC
Law for
of Sines
and Law
oflengths
Cosines
Use
Items 4–6.
Round
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.
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8-5 Law of Sines and Law of Cosines
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?
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8-5 Law of Sines and Law of Cosines
•Home Work PG# 555
•18-36 evens,
40,42,46,48,50,51,
52,53
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