follow the steps to find the area of the shaded region.
use trigonometry to find the height of the triangle.
hint: use sohcahtoa
$h = ?\text{ cm}$

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Right Triangle Trigonometry", "Sine Ratio" ], "new_concepts": [], "current_concepts": [ "Right Triangle Trigonometry", "Sine Ratio", "Area of Circular Segment" ] } ## Identify the right triangle and given values Using the **Right Triangle Trigonometry** knowledge point $$ \begin{aligned} &\text{Hypotenuse } (c) = 8\text{ cm}\ &\text{Angle } (\theta) = 51^\circ\ &\text{Opposite side } = h \end{aligned} $$ ## Apply the sine ratio to solve for h Using the **Sine Ratio** knowledge point $$ \begin{aligned} &\sin(51^\circ) = \frac{h}{8}\ &h = 8 \cdot \sin(51^\circ)\ &h \approx 8 \cdot 0.7771 \approx 6.22\text{ cm} \end{aligned} $$ Follow the steps to find the area of the shaded region. Use trigonometry to find the height of the triangle. Hint: Use SOHCAHTOA $h =$ $6.22$ cm { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Right Triangle Trigonometry" ] }

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Question

Explanation:

Identify the right triangle and given values

Apply the sine ratio to solve for h

Answer: