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What is the width of the pond, East to West? Round answer to nearest whole foot! using Law of Cosines first

To determine the width of the pond from East to West using the Law of Cosines, we will consider the triangle formed by the points at the 950 ft, 1000 ft, and 60° angle. The width of the pond corresponds to the side opposite the 60° angle.

### Step 1: Use the Law of Cosines
The Law of Cosines states:

\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]

Where:
- \( c \) is the side opposite the angle (which represents the width of the pond).
- \( a = 950 \, \text{ft} \)
- \( b = 1000 \, \text{ft} \)
- \( C = 60^\circ \)

### Step 2: Substitute the values into the Law of Cosines

\[
c^2 = 950^2 + 1000^2 - 2 \times 950 \times 1000 \times \cos(60^\circ)
\]

Given that \(\cos(60^\circ) = 0.5\):

\[
c^2 = 950^2 + 1000^2 - 2 \times 950 \times 1000 \times 0.5
\]

\[
c^2 = 902500 + 1000000 - 950000
\]

\[
c^2 = 950500
\]

\[
c = \sqrt{950500}
\]

### Step 3: Calculate the square root

\[
c \approx 975.0 \, \text{ft}
\]

So, the width of the pond from East to West is approximately **975 feet**.

Would you like more details or have any other questions?

Here are 5 related questions to further explore:
1. How would the width change if the angle were larger than 60°?
2. Can you find the area of the triangle using the width calculated?
3. How does the Law of Cosines compare to the Pythagorean theorem in this context?
4. What if the lengths were different; how would it affect the result?
5. How would you determine the perimeter of the pond?

**Tip:** The Law of Cosines is a powerful tool for solving triangles that are not right-angled, allowing you to find unknown sides or angles when you have enough information.

What is the width of the pond, East to West? Round answer to nearest whole foot! using Law of Cosines first

Learn how to find the width of a pond from East to West using the Law of Cosines. This problem involves a triangle with sides of 950 ft, 1000 ft, and a 60° angle. Follow a step-by-step solution to determine the pond's width, rounded to the nearest whole foot. Suitable for high school students in Grades 10-12.

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