https://file.aiquickdraw.com/mathbot/file/172874428340256bkz2xd.jpg

To find the area of triangle \( ABC \), we can use the formula for the area of a triangle when two sides and the included angle are known. This formula is:

\[
\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)
\]

Where:
- \( a \) and \( b \) are the lengths of two sides.
- \( C \) is the angle between those sides.

From the image:
- \( a = 25 \, \text{cm} \)
- \( b = 24 \, \text{cm} \)
- \( C = 73^\circ \)

Now, plug the values into the formula:

\[
\text{Area} = \frac{1}{2} \times 25 \times 24 \times \sin(73^\circ)
\]

First, calculate \( \sin(73^\circ) \):

\[
\sin(73^\circ) \approx 0.9563
\]

Now calculate the area:

\[
\text{Area} = \frac{1}{2} \times 25 \times 24 \times 0.9563 \approx 287.0 \, \text{cm}^2
\]

So, the area of the triangle is approximately \( 287.0 \, \text{cm}^2 \).

Would you like more details on this solution or have any further questions?

Here are 5 related questions you might find interesting:
1. How can you find the third side of a triangle using the Law of Cosines?
2. What is the Law of Sines, and how does it apply to triangles?
3. How would the area formula change if you only had two sides and no angle?
4. How can you calculate the perimeter of the triangle \( ABC \)?
5. How does the sine function behave as angles approach 90 degrees?

**Tip:** In geometry, always check if the given angle is between the known sides when applying trigonometric formulas for areas.

Find the area of the triangle ABC with sides 25 cm, 24 cm, and an included angle of 73°.

Learn how to find the area of a triangle with sides 25 cm, 24 cm, and an included angle of 73°. This example uses the sine rule for area calculation, a key concept in trigonometry and geometry. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation