Math Problem Statement
A triangular swimming pool measures
4545
ft on one side and
32.232.2
ft on another side. The two sides form an angle that measures
40.740.7degrees°.
How long is the third side?
Question content area bottom
Part 1
The length of the third side is
enter your response here
ft.
(Simplify your answer. Type an integer or a decimal. Round to the nearest tenth if needed.)
Solution
To calculate the length of the third side of the triangle, we can use the Law of Cosines. The formula is:
Where:
- and are the known sides of the triangle
- is the angle between the two known sides
- is the third side we want to calculate
Given:
Step 1: Apply the formula
Step 2: Compute values
- Compute
Substituting:
Step 3: Take the square root
Final Answer:
The length of the third side is approximately 29.3 ft.
Would you like more details or assistance with related questions?
Here are five related questions for exploration:
- What is the formula for the Law of Cosines, and when is it used?
- How do you calculate the area of a triangle with two sides and the included angle?
- What are some real-world applications of the Law of Cosines?
- How does the Law of Cosines generalize the Pythagorean theorem?
- How can you calculate the remaining angles in the triangle after finding the third side?
Tip: Always keep your calculator in degree mode when working with angles measured in degrees.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Triangle Geometry
Law of Cosines
Formulas
c² = a² + b² - 2ab * cos(C)
Theorems
Law of Cosines
Suitable Grade Level
Grades 10-12
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