Triangle Applications and Vectors flashcards

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What is corresponding side-angle pairs?Law of Sines and the Ambiguous Case: A relationship between each triangle side and the sine of its opposite angle.
What condition or caution matters when using corresponding side-angle pairs?Law of Sines and the Ambiguous Case: Pair each side with its opposite angle, not an adjacent angle.
What is ssa feasibility and ambiguity?Law of Sines and the Ambiguous Case: An SSA situation that can determine zero, one, or two triangles.
What condition or caution matters when using ssa feasibility and ambiguity?Law of Sines and the Ambiguous Case: The supplementary angle must also pass the triangle angle-sum check.
What is included angles and side lengths?Law of Cosines and Triangle Area: A side-angle relation valid for any triangle, especially SAS and SSS data.
What condition or caution matters when using included angles and side lengths?Law of Cosines and Triangle Area: The cosine angle is between the two sides in the product term.
What is area from two sides and an angle?Law of Cosines and Triangle Area: Triangle area calculated using two sides and their included angle.
What condition or caution matters when using area from two sides and an angle?Law of Cosines and Triangle Area: Use the included angle and report square units.
What is vector addition and scalar multiplication?Vectors and Components: A directed quantity represented by signed coordinate components.
What condition or caution matters when using vector addition and scalar multiplication?Vectors and Components: Vector addition combines corresponding components.
What is magnitude and unit vectors?Vectors and Components: The nonnegative length of a vector and its normalized direction.
What condition or caution matters when using magnitude and unit vectors?Vectors and Components: The zero vector cannot be normalized because its magnitude is zero.
What is dot product and orthogonality?Dot Products and Projections: A scalar product connecting vector components with their included angle.
What condition or caution matters when using dot product and orthogonality?Dot Products and Projections: The nonzero-vector condition matters when inferring an angle.
What is vector projection?Dot Products and Projections: The part of a vector parallel to another nonzero vector’s direction.
What condition or caution matters when using vector projection?Dot Products and Projections: Vector projection differs from the scalar component along a direction.