right triangle xyz has a right angle at vertex y and a hypotenuse that measures 24 cm. angle zxy measures 70°.
what is the length of line segment xy? round to the nearest tenth.
8.2 cm
8.7 cm
22.6 m
25.5 cm

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Right Triangle Trigonometry", "Trigonometric Ratios" ], "new_concepts": [], "current_concepts": [ "Right Triangle Trigonometry", "Trigonometric Ratios" ] } ## Identify given values and trigonometric relationship $$ \begin{aligned} &\text{Hypotenuse } XZ = 24\text{ cm} \ &\text{Angle } \angle ZXY = 70^\circ \ &\cos(\angle ZXY) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{XY}{XZ} \end{aligned} $$ ## Solve for the length of segment XY $$ \begin{aligned} &XY = XZ \cdot \cos(70^\circ) \ &XY = 24 \cdot \cos(70^\circ) \end{aligned} $$ ## Calculate the numerical value $$ \begin{aligned} &\cos(70^\circ) \approx 0.34202 \ &XY \approx 24 \cdot 0.34202 \approx 8.2085\text{ cm} \ &XY \approx 8.2\text{ cm} \end{aligned} $$

(A) 8.2 cm

(B) 8.7 cm

(C) 22.6 m

(D) 25.5 cm

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Question

Explanation:

Identify given values and trigonometric relationship

Solve for the length of segment XY

Calculate the numerical value

Answer: