question 5 (1 point)

complete the ratios for the given angle.

$\sin(r) = \frac{\text{blank 1}}{\text{blank 2}}$
$\cos(r) = \frac{\text{blank 3}}{\text{blank 4}}$
$\tan(r) = \frac{\text{blank 5}}{\text{blank 6}}$

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Question

question 5 (1 point)

complete the ratios for the given angle.

$\sin(r) = \frac{\text{blank 1}}{\text{blank 2}}$
$\cos(r) = \frac{\text{blank 3}}{\text{blank 4}}$
$\tan(r) = \frac{\text{blank 5}}{\text{blank 6}}$

blank 1:
blank 2:
blank 3:
blank 4:
blank 5:
blank 6:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Trigonometric Ratios" ], "new_concepts": [], "current_concepts": [ "Trigonometric Ratios", "Right Triangle Trigonometry" ] } ## Identify sides relative to angle R $$ \begin{aligned} &\text{Opposite side } (TS) = 56\ &\text{Adjacent side } (TR) = 90\ &\text{Hypotenuse } (SR) = 106 \end{aligned} $$ ## Calculate and simplify trigonometric ratios $$ \begin{aligned} &\sin(R) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{56}{106} = \frac{28}{53}\ &\cos(R) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{90}{106} = \frac{45}{53}\ &\tan(R) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{56}{90} = \frac{28}{45} \end{aligned} $$ ## Match values to blanks $$ \begin{aligned} &\text{Blank 1 (numerator of } \sin(R)\text{)} = 28\ &\text{Blank 2 (denominator of } \sin(R)\text{)} = 53\ &\text{Blank 3 (numerator of } \cos(R)\text{)} = 45\ &\text{Blank 4 (denominator of } \cos(R)\text{)} = 53\ &\text{Blank 5 (numerator of } \tan(R)\text{)} = 28\ &\text{Blank 6 (denominator of } \tan(R)\text{)} = 45 \end{aligned} $$ Complete the ratios for the given angle. $\sin(R) = \frac{\text{28}}{\text{53}}$ $\cos(R) = \frac{\text{45}}{\text{53}}$ $\tan(R) = \frac{\text{28}}{\text{45}}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Trigonometric Ratios" ] }

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Question

Explanation:

Identify sides relative to angle R

Calculate and simplify trigonometric ratios

Match values to blanks

Answer: