triangle abc is a right triangle, and $\sin(53^{\circ}) = \frac{4}{x}$. solve for x and round to the nearest whole number.

which equation correctly uses the value of x to represent the cosine of angle a?

$\cos(53^{\circ}) = \frac{4}{x}$
$\cos(53^{\circ}) = \frac{y}{5}$
$\cos(53^{\circ}) = \frac{x}{4}$
$\cos(53^{\circ}) = \frac{5}{y}$

Question

triangle abc is a right triangle, and $\sin(53^{\circ}) = \frac{4}{x}$. solve for x and round to the nearest whole number.

which equation correctly uses the value of x to represent the cosine of angle a?

$\cos(53^{\circ}) = \frac{4}{x}$
$\cos(53^{\circ}) = \frac{y}{5}$
$\cos(53^{\circ}) = \frac{x}{4}$
$\cos(53^{\circ}) = \frac{5}{y}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Right Triangle Trigonometry", "Trigonometric Ratios" ], "current_concepts": [ "Right Triangle Trigonometry", "Trigonometric Ratios" ] } ## Solve for x using the sine ratio $$ \begin{aligned} \sin(53^\circ) &= \frac{4}{x} \ x &= \frac{4}{\sin(53^\circ)} \ x &\approx \frac{4}{0.7986} \approx 5.008 \ x &\approx 5 \end{aligned} $$ ## Determine the cosine ratio for angle A $$ \begin{aligned} \cos(A) &= \frac{\text{Adjacent}}{\text{Hypotenuse}} \ \cos(53^\circ) &= \frac{y}{x} \ \text{Substitute } x = 5: \ \cos(53^\circ) &= \frac{y}{5} \end{aligned} $$

(A) $\cos(53^\circ) = \frac{4}{x}$

(B) $\cos(53^\circ) = \frac{y}{5}$

(C) $\cos(53^\circ) = \frac{x}{4}$

(D) $\cos(53^\circ) = \frac{5}{y}$

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

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Question

Explanation:

Solve for x using the sine ratio

Determine the cosine ratio for angle A

Answer: