Geometry (ACT Prep) - Law of Sines and Cosines
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Mathematics
•
9th - 10th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the Law of Sines?
Back
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides: Sin(A)/a = Sin(B)/b = Sin(C)/c.
2.
FLASHCARD QUESTION
Front
What is the Law of Cosines?
Back
The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles: c² = a² + b² - 2ab * cos(C).
3.
FLASHCARD QUESTION
Front
How do you find the length of a side using the Law of Sines?
Back
To find a side length, use the formula: a = b * (Sin(A)/Sin(B)), where A and B are the angles opposite sides a and b.
4.
FLASHCARD QUESTION
Front
How do you find an angle using the Law of Sines?
Back
To find an angle, rearrange the Law of Sines: A = sin⁻¹(a * Sin(B)/b).
5.
FLASHCARD QUESTION
Front
What is the formula for the area of a triangle using the Law of Sines?
Back
Area = (1/2) * a * b * Sin(C), where a and b are two sides and C is the included angle.
6.
FLASHCARD QUESTION
Front
What is the relationship between the angles and sides in a triangle?
Back
In any triangle, the larger the angle, the longer the side opposite that angle.
7.
FLASHCARD QUESTION
Front
What is the sine of an angle in a right triangle?
Back
In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse: Sin(θ) = Opposite/Hypotenuse.
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