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Which side forms an opposite pair with angle $B$?

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Side $b$.

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The interior angles of a triangle sum to $\\text{[...]}$.

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The interior angles of a triangle sum to $\\boxed{180^\\circ}$.

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Which rule is suggested by a known opposite side-angle pair?

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The sine rule.

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Which rule should be used with two known sides and their included angle?

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The cosine rule.

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Which rule should be used to find an angle from all three sides?

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The cosine rule.

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Triangulation determines distances using measured angles and [ ].

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Triangulation determines distances using measured angles and a known baseline.

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For any triangle, the sine rule is $$\\text{[...]}$$.

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For any triangle, the sine rule is $$\\boxed{\\frac{a}{\\sin A}=\\frac{b}{\\sin B}=\\frac{c}{\\sin C}}$$.

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Which angle is included between sides $a$ and $b$?

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Angle $C$.

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The cosine rule for side $c$ is $$\\text{[...]}$$.

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The cosine rule for side $c$ is $$\\boxed{c^2=a^2+b^2-2ab\\cos C}$$.

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How can the relative sizes of sides and opposite angles be checked?

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The largest side must be opposite the largest angle.

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Why is only the positive square root used when finding a side?

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A length cannot be negative.

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Which inverse function finds an angle from its sine?

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$\\sin^{-1}$.

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When all three sides are known, angle $C$ satisfies $$\\text{[...]}$$.

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When all three sides are known, angle $C$ satisfies $$\\boxed{\\cos C=\\frac{a^2+b^2-c^2}{2ab}}$$.

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When can the ambiguous sine-rule case occur?

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When two sides and a non-included angle are known.

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If inverse sine gives an acute angle $\\theta$, the possible second angle is $\\text{[...]}$.

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If inverse sine gives an acute angle $\\theta$, the possible second angle is $\\boxed{180^\\circ-\\theta}$.

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Why can the sine rule produce two possible an

1.7.6 Sine and cosine rules Flashcards

1.7.6 Sine and cosine rules Flashcards