https://file.aiquickdraw.com/mathbot/file/1726496920898un3bhenn.jpg

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.

What is the best estimate for the area of △ABC?

Find the area of triangle ABC using trigonometry. Given a right triangle with AB = 10 cm, angle BAC = 26°, and angle ACB = 90°, apply trigonometric functions to estimate the area. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation