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Example Questions
Example Question #89 : Trigonometry
In ,
,
, and
. To the nearest tenth, what is
?
Possible Answers:
A triangle with these sidelengths cannot exist.
Correct answer:
Explanation:
By the Triangle Inequality, this triangle can exist, since .
By the Law of Cosines:
Substitute the sidelengths and solve for :
Example Question #1 : Law Of Cosines
A triangle has sides of length 12, 17, and 22. Of the measures of the three interior angles, which is the greatest of the three?
Possible Answers:
Correct answer:
Explanation:
We can apply the Law of Cosines to find the measure of this angle, which we will call :
The widest angle will be opposite the side of length 22, so we will set:
,
,
Example Question #11 : Graphing The Sine And Cosine Functions
In ,
,
, and
. To the nearest tenth, what is
?
Possible Answers:
A triangle with these characteristics cannot exist.
Correct answer:
Explanation:
By the Law of Cosines:
or, equivalently,
Substitute:
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