the picture shows a triangular island:
which expression shows the value of q? (1 point)
$r \cos 55^\circ$
$r \sin 55^\circ$
$\frac{s}{\sin 55^\circ}$
$\frac{s}{\cos 55^\circ}$

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Right Triangle Trigonometry" ], "new_concepts": [], "current_concepts": [ "Right Triangle Trigonometry", "Cosine Ratio" ] } ## Identify the triangle parts Using the *Right Triangle Trigonometry* knowledge point $$ \begin{aligned} &\text{Hypotenuse} = q\ &\text{Adjacent side to } 55^\circ = s\ &\text{Opposite side to } 55^\circ = r \end{aligned} $$ ## Set up the trigonometric ratio Using the *Right Triangle Trigonometry* knowledge point $$ \begin{aligned} &\cos(55^\circ) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{s}{q} \end{aligned} $$ ## Solve for q Using the *Right Triangle Trigonometry* knowledge point $$ \begin{aligned} &q \cdot \cos(55^\circ) = s\ &q = \frac{s}{\cos(55^\circ)} \end{aligned} $$

(A) $r \cos 55^\circ$

(B) $r \sin 55^\circ$

(C) $\frac{s}{\sin 55^\circ}$

(D) $\frac{s}{\cos 55^\circ}$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the triangle parts

Set up the trigonometric ratio

Solve for q

Answer: