find the value of the variable. if your answer is not an integer, leave it in simplest radical form.

not drawn to scale

$5\sqrt{3}$
$5\sqrt{2}$
$\frac{5\sqrt{3}}{2}$
$\frac{5\sqrt{2}}{2}$

Question

find the value of the variable. if your answer is not an integer, leave it in simplest radical form.

not drawn to scale

$5\sqrt{3}$
$5\sqrt{2}$
$\frac{5\sqrt{3}}{2}$
$\frac{5\sqrt{2}}{2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Special Right Triangles", "Trigonometric Ratios" ], "new_concepts": [], "current_concepts": [ "Special Right Triangles", "Trigonometric Ratios" ] } ## Identify the given values and triangle properties $$ \begin{aligned} &\theta = 45^\circ \ &\text{Hypotenuse} = 5 \ &\text{Opposite side } (x) = \text{unknown} \end{aligned} $$ ## Apply trigonometric ratio or special right triangle rules $$ \begin{aligned} &\sin(45^\circ) = \frac{\text{Opposite}}{\text{Hypotenuse}} \ &\frac{\sqrt{2}}{2} = \frac{x}{5} \end{aligned} $$ ## Solve for the variable x $$ x = \frac{5\sqrt{2}}{2} $$

(A) $5\sqrt{3}$

(B) $5\sqrt{2}$

(C) $\frac{5\sqrt{3}}{2}$

(D) $\frac{5\sqrt{2}}{2}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Special Right Triangles" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values and triangle properties

Apply trigonometric ratio or special right triangle rules

Solve for the variable x

Answer: