Law of Cosines Quiz Form
Test your understanding of the Law of Cosines. Answer all questions to the best of your ability.
What is the correct formula for the Law of Cosines?
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c² = a² + b² - 2ab cos(C)
c² = a² + b² + 2ab cos(C)
c² = a² + b² - 2ab sin(C)
c² = a² + b² + 2ab sin(C)
In which type of triangle is the Law of Cosines most useful?
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Equilateral triangle
Right triangle
Scalene triangle
Isosceles triangle
Given triangle ABC with sides a = 7, b = 9, and angle C = 60°, what is the length of side c? (Round to two decimal places)
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Select all situations where the Law of Cosines can be applied.
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To find the third side when two sides and the included angle are known
To find an angle when all three sides are known
To find an angle when only two sides are known
To find the area of a triangle
If a triangle has sides a = 5, b = 8, c = 10, what is the measure of angle C (opposite side c)? (Round to nearest degree)
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Show your work for the previous problem. (Explain your calculation steps or write the equation you used.)
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Which of the following is NOT a possible use of the Law of Cosines?
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Finding a side when two sides and the included angle are known
Finding an angle when all three sides are known
Finding the height of a triangle given base and area
Solving for all angles in a right triangle
A triangle has sides of length 6, 8, and 10. Which angle is the largest?
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Angle opposite side 6
Angle opposite side 8
Angle opposite side 10
All angles are equal
If you know all three sides of a triangle, which law should you use to find an angle?
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Law of Sines
Law of Cosines
Pythagorean Theorem
Law of Tangents
Briefly explain, in your own words, when you would choose to use the Law of Cosines instead of the Law of Sines.
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