Find the area of the triangle having the given measurements.

Upper A equals 48 degrees comma b equals 16 feet comma c equals 39 feetA=48°, b=16 feet, c=39 feet

Question content area bottom

Part 1

Areaalmost equals≈enter your response here 

square feet 

          ​ (Round to the nearest whole number as​ needed.)

To find the area of the triangle given the angle \( A \) and sides \( b \) and \( c \), we can use the formula:

\[
\text{Area} = \frac{1}{2}bc \sin A
\]

where:
- \( A = 48^\circ \)
- \( b = 16 \) feet
- \( c = 39 \) feet

First, we calculate \( \sin 48^\circ \):

\[
\sin 48^\circ \approx 0.7431
\]

Now substituting the values into the area formula:

\[
\text{Area} = \frac{1}{2} \times 16 \times 39 \times \sin(48^\circ)
\]
\[
\text{Area} = \frac{1}{2} \times 16 \times 39 \times 0.7431
\]
\[
\text{Area} = 8 \times 39 \times 0.7431
\]
\[
\text{Area} \approx 8 \times 29.0289
\]
\[
\text{Area} \approx 232.2312
\]

Rounding to the nearest whole number:

\[
\text{Area} \approx 232 \text{ square feet}
\]

### Final Answer:
The area of the triangle is approximately **232 square feet**.

### Do you have any questions or need further details? Here are some related questions to consider:
1. What are other methods to find the area of a triangle?
2. How would the area change if angle \( A \) were different?
3. Can the Law of Cosines be applied to this triangle?
4. What if one of the sides was longer than the sum of the other two?
5. How do you calculate the angles of a triangle when given all three sides?

### Tip:
To deepen your understanding of triangle properties, consider exploring the relationships between angles and sides, especially the Law of Sines and Law of Cosines.

Find the area of the triangle having the given measurements: A=48°, b=16 feet, c=39 feet.

Discover how to calculate the area of a triangle with an angle of 48 degrees and sides measuring 16 feet and 39 feet. This solution involves trigonometric functions and is ideal for high school geometry students.

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