Question

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}\\)

Explanation:

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<reasoning>

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
\[

$$\begin{aligned} &\sin(51^\circ) = \frac{h}{8}\\ &h = 8 \cdot \sin(51^\circ)\\ &h \approx 8 \cdot 0.7771 \approx 6.22\text{ cm} \end{aligned}$$

\]
</reasoning>

<answer>
Follow the steps to find the area of the shaded region.
Use trigonometry to find the height of the triangle.
Hint: Use SOHCAHTOA
\(h =\) <blank>\(6.22\)</blank> cm
</answer>

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Answer:

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<reasoning>

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
\[

$$\begin{aligned} &\sin(51^\circ) = \frac{h}{8}\\ &h = 8 \cdot \sin(51^\circ)\\ &h \approx 8 \cdot 0.7771 \approx 6.22\text{ cm} \end{aligned}$$

\]
</reasoning>

<answer>
Follow the steps to find the area of the shaded region.
Use trigonometry to find the height of the triangle.
Hint: Use SOHCAHTOA
\(h =\) <blank>\(6.22\)</blank> cm
</answer>

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