Understanding Law of Cosines
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Beginner
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Beginner Explanation
In a right triangle when $\angle C = 90^\circ$, $\cos C = 0$. Substituting into the Law of Cosines $c^2 = a^2 + b^2 - 2ab \cos C$ gives $c^2 = a^2 + b^2$, which is the Pythagorean theorem.
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Practice Problems
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1
Quick Quiz
Single Choice Quiz
Beginner
If $a = 3$, $b = 4$, and $\angle C = 90^\circ$, what is $c$?
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2
Real-World Problem
Question Exercise
Intermediate
Teenager Scenario
A triangle with sides $a = 5$, $b = 6$, and $\angle C = 60^\circ$.
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3
Thinking Challenge
Thinking Exercise
Intermediate
Think About This
Given $a = 7$, $b = 9$, and $\angle C = 45^\circ$, find $c$.
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4
Challenge Quiz
Single Choice Quiz
Advanced
In triangle $\triangle ABC$ with $a = 8$, $b = 10$, and $\angle C = 120^\circ$, find $c$. Round your answer to the nearest whole number.
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