What is the area of the given triangle? Round to the nearest whole number. 57 ft A B C D 38° 1088 square feet 1483 square feet 1577 square feet 1767 square feet 62 ft
What is the area of the given triangle? Round to the nearest whole number. 57 ft A B C D 38° 1088 square feet 1483 square feet 1577 square feet 1767 square feet 62 ft
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![### Question 8
**What is the area of the given triangle? Round to the nearest whole number.**
A triangle is provided with the following measurements:
- One side is labeled as 57 feet
- Another side is labeled as 62 feet
- An angle between these two sides is labeled as 38°
#### Answer Choices:
A. 1088 square feet
B. 1483 square feet
C. 1577 square feet
D. 1767 square feet
#### Solution:
To find the area of a triangle when two sides and the included angle are known, use the formula:
\[ \text{Area} = \frac{1}{2}ab\sin(C) \]
Where:
- \( a \) and \( b \) are the lengths of the two sides
- \( C \) is the included angle
Substitute the given values:
\[ a = 57 \, \text{ft}, b = 62 \, \text{ft}, \text{and } C = 38^\circ \]
\[ \text{Area} = \frac{1}{2} \times 57 \times 62 \times \sin(38^\circ) \]
By calculating the sine of 38 degrees and solving,
\[ \sin(38^\circ) \approx 0.6157 \]
\[ \text{Area} \approx \frac{1}{2} \times 57 \times 62 \times 0.6157 \]
\[ \text{Area} \approx 1087.76 \, \text{square feet} \]
Rounded to the nearest whole number,
\[ \text{Area} \approx 1088 \, \text{square feet} \]
So, the correct answer is:
**A. 1088 square feet**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F075db94c-9df1-4bd0-8bd8-7247d457f29a%2F93934ed6-113c-42ab-8229-0a7df66db87f%2Ftti4vck_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 8
**What is the area of the given triangle? Round to the nearest whole number.**
A triangle is provided with the following measurements:
- One side is labeled as 57 feet
- Another side is labeled as 62 feet
- An angle between these two sides is labeled as 38°
#### Answer Choices:
A. 1088 square feet
B. 1483 square feet
C. 1577 square feet
D. 1767 square feet
#### Solution:
To find the area of a triangle when two sides and the included angle are known, use the formula:
\[ \text{Area} = \frac{1}{2}ab\sin(C) \]
Where:
- \( a \) and \( b \) are the lengths of the two sides
- \( C \) is the included angle
Substitute the given values:
\[ a = 57 \, \text{ft}, b = 62 \, \text{ft}, \text{and } C = 38^\circ \]
\[ \text{Area} = \frac{1}{2} \times 57 \times 62 \times \sin(38^\circ) \]
By calculating the sine of 38 degrees and solving,
\[ \sin(38^\circ) \approx 0.6157 \]
\[ \text{Area} \approx \frac{1}{2} \times 57 \times 62 \times 0.6157 \]
\[ \text{Area} \approx 1087.76 \, \text{square feet} \]
Rounded to the nearest whole number,
\[ \text{Area} \approx 1088 \, \text{square feet} \]
So, the correct answer is:
**A. 1088 square feet**
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