Laws%20of%20Sines%20and%20Cosines

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Laws of Sines and Cosines

• Sections 6.1 and 6.2

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Objectives

• Apply the law of sines to determine the lengths
  of side and measures of angle of a triangle.
• Solve word problems requiring the law of sines.
• Apply the law of cosines to determine the lengths
  of side and measures of angle of a triangle.
• Solve word problems requiring the law of cosines.
  
• Solve a word problem requiring Heron's formula.

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Formulas

• Law of sines
• Law of cosines
• Herons formula

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Law of Sines
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Law of Cosines
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Use the Law of Sines to find the value of the
side x.
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Use the Law of Cosines to find the value of the
side x.
x
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Two ships leave a harbor at the same time,
traveling on courses that have an angle of 140
degrees between them.  If the first ship travels
at 26 miles per hour and the second ship travels
at 34 miles per hour, how far apart are the two
ships after 3 hours?
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The path of a satellite orbiting the earth causes
it to pass directly over two tracking stations A
and B, which are 48 miles apart.  When the
satellite is on one side of the two stations, the
angles of elevation at A and B are measured to be
87 degrees and 84 degrees.  How far is the
satellite from station A?  How far is the
satellite above the ground?
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(No Transcript)
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A triangular parcel of land has sides of length
680 feet, 320 feet, and 802 feet.  What is the
area of the parcel of land?  If land is valued at
2100 per acre (1 acre is 43560 square feet),
what is the value of the parcel of land.
Herons Formula