To solve the problem, we need to estimate the area of triangle $\triangle ABC$ based on the information in the image. Here's what we have:

1. $AB = 10 \, \text{cm}$
2. $\angle BAC = 26^\circ$
3. $\angle ACB = 90^\circ$, making this a right triangle.

The formula for the area of a triangle is:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

In this case:

• The base is $AC$.
• The height is $AB$, since it's the hypotenuse in this context.

To calculate the area, we'll need to first find the length of side $AC$ using trigonometry. Since $\angle BAC = 26^\circ$, we can use the cosine function:

$\cos(26^\circ) = \frac{AC}{AB}$

Thus:

$AC = AB \times \cos(26^\circ)$

After finding $AC$, we'll compute the area. Let's proceed with the calculation.The area of triangle $\triangle ABC$ is approximately $44.94 \, \text{cm}^2$.

Based on the provided answer choices, the closest option is:

• C: 43.8 cm²

Would you like further details, or do you have any other questions?

Here are 5 related questions to deepen understanding:

1. How would you calculate the length of side $BC$ in this triangle?
2. What trigonometric function would you use to find $BC$?
3. Can you calculate the perimeter of $\triangle ABC$?
4. What would the area of the triangle be if $\angle BAC$ was $45^\circ$?
5. How does the area change if side $AB$ is doubled?

Tip: For right triangles, trigonometric ratios like sine, cosine, and tangent are essential for finding unknown side lengths based on angles.