Download geometry module 2 lesson 33 applying the laws of sines and cosines

GEOMETRY
MODULE 2 LESSON 33
APPLYING THE LAWS OF SINES AND COSINES
OPENING EXERCISE
Complete the Opening Exercise in your workbook.
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MOD2 L33
Law of Sines
Law of Cosines
Pythagorean Theorem
Law of Sines or Law of Cosines
Law of Sines
1
PRACTICE
Example 1: Find the missing side length in ∆𝐴𝐵𝐶.
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Which method should we use to find length AB?
Explain.
The law of sines can be used because we are given information about two of the angles and one
side. We can use the triangle sum theorem to find the measure of angle C.
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Why can’t we use the Pythagorean Theorem with this problem?
We can only use the Pythagorean Theorem with right triangles. The given triangle is not a right
triangle.
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Why can’t we use the law of cosines with this problem?
The law of cosines requires that we know the lengths of two sides of the triangle. We are only
given information about the length of one side.
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Write the equation to find the length of AB.
sin 75 sin 23
=
2.93
𝐴𝐵
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Find AB and round the length to the tenths place.
sin 75 sin 23
=
2.93
𝐴𝐵
𝐴𝐵 sin 75 = 2.93 sin 23
𝐴𝐵 =
2.93 sin 23
= 1.18
sin 75
𝐴𝐵 = 1.2
MOD2 L33
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Example 2: Find the missing side length in ∆𝐴𝐵𝐶.
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Which method should we use to find length AC?
Explain.
We do not have enough information to use the law
of sines because we do not have enough information to write any of the ratios related to the law of
sines. We can use law of cosines because we are given two side lengths and the included angle.
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Write the equation that to find the length of AC.
𝑥 2 = 5.812 + 5.952 − 2(5.81)(5.95) cos 16
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Find AC and round the length to the tenths place.
𝑥 2 = 5.812 + 5.952 − 2(5.81)(5.95) cos 16
𝑥 = √5.812 + 5.952 − 2(5.81)(5.95) cos 16
𝑥 = 1.64
𝑥 = 1.6
SUMMARY
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Pythagorean Theorem: Use when solving a right triangle. At least one complementary angle
measure and one side measure must be known.
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Law of Sines: Use to solve acute (and obtuse triangles). There are two cases in which law of sines
should be used – (1) when two angles and one side are known and (2). *when two sides and an
angle are known. *This is a special case involving inverse trig functions.
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Law of Cosines: Use to solve acute (and obtuse triangles). Law of cosines should be used when
two sides and the included angle is known.
GROUP ACTIVITY
Complete Exercises 1, 2, and 3 in your workbook. Turn in by the end of class.
MOD2 L33
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