Unit 12 Mastery Check

A right triangle has legs $5$ and $12$. Find all six trig ratios for the angle opposite side $5$.

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A right triangle has legs $5$ and $12$. Find all six trig ratios for the angle opposite side $5$.

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State the defining idea behind right triangles and trigonometric ratios in one precise sentence.

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For right triangles and trigonometric ratios, what condition or domain restriction must remain visible in the solution?

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A $20-meter$ cable makes $a 58-degree$ angle with level ground. Find vertical rise.

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A $20-meter$ cable makes $a 58-degree$ angle with level ground. Find vertical rise.

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State the defining idea behind right-triangle applications in one precise sentence.

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For right-triangle applications, what condition or domain restriction must remain visible in the solution?

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When is the Law of Sines directly useful without ambiguity?

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When is the Law of Sines directly useful without ambiguity?

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State the defining idea behind the law of sines in one precise sentence.

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For the law of sines, what condition or domain restriction must remain visible in the solution?

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For acute A, state the two-triangle condition in terms of h, a, and $b$.

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For acute A, state the two-triangle condition in terms of h, a, and $b$.

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State the defining idea behind the ambiguous ssa case in one precise sentence.

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For the ambiguous ssa case, what condition or domain restriction must remain visible in the solution?

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Which angle should be found first in an SSS triangle and why?

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Which angle should be found first in an SSS triangle and why?

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State the defining idea behind the law of cosines in one precise sentence.

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For the law of cosines, what condition or domain restriction must remain visible in the solution?

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A triangle has area $30,$ sides $8$ and $10$ enclosing angle C. Find possible C values.

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A triangle has area $30,$ sides $8$ and $10$ enclosing angle C. Find possible C values.

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State the defining idea behind triangle area formulas in one precise sentence.

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For triangle area formulas, what condition or domain restriction must remain visible in the solution?

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Convert bearing $S20W$ to a standard mathematical angle.

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Convert bearing $S20W$ to a standard mathematical angle.

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State the defining idea behind bearings and navigation in one precise sentence.

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For bearings and navigation, what condition or domain restriction must remain visible in the solution?

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Find magnitude and direction of$$<3,-3>$$

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Find magnitude and direction of$$<3,-3>$$

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State the defining idea behind vectors geometrically and in components in one precise sentence.

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For vectors geometrically and in components, what condition or domain restriction must remain visible in the solution?

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Find a vector of magnitude $10$ in the direction of $<1,2>$.

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Find a vector of magnitude $10$ in the direction of $<1,2>$.

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State the defining idea behind vector operations, magnitude, direction, and unit vectors in one precise sentence.

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For vector operations, magnitude, direction, and unit vectors, what condition or domain restriction must remain visible in the solution?

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