if $\cos f^\circ = \frac{4}{9}$ and the measure of $\overline{xw}$ is 16 units, what is the measure of $\overline{xy}$? (4 points)

16 units
27 units
30 units
36 units

Question

if $\cos f^\circ = \frac{4}{9}$ and the measure of $\overline{xw}$ is 16 units, what is the measure of $\overline{xy}$? (4 points)

16 units
27 units
30 units
36 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Right Triangle Trigonometry", "Cosine Ratio" ], "new_concepts": [], "current_concepts": [ "Right Triangle Trigonometry", "Cosine Ratio" ] } ## Identify the given values and trigonometric ratio $$ \begin{aligned} &\triangle XYW \text{ is a right triangle with } \angle XWY = 90^\circ\ &\cos(f^\circ) = \frac{4}{9}\ &XW = 16 \end{aligned} $$ ## Apply the cosine ratio formula $$ \begin{aligned} &\cos(f^\circ) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{XW}{XY}\ &\frac{4}{9} = \frac{16}{XY} \end{aligned} $$ ## Solve for the hypotenuse XY $$ \begin{aligned} &4 \cdot XY = 16 \cdot 9\ &XY = \frac{144}{4} = 36 \end{aligned} $$

16 units

27 units

30 units

36 units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Right Triangle Trigonometry" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values and trigonometric ratio

Apply the cosine ratio formula

Solve for the hypotenuse XY

Answer: