Question

Clarksville is 54 miles due north of the airport, and Sparrowtown is due east of the airport. If the distance between Clarksville and Sparrowtown is 90 miles, how far is Sparrowtown from the airport?

Answer 1

So, Sparrowtown is 72 miles from the airport.

Explanation:

To find the distance from Sparrowtown to the airport, you can use the Pythagorean theorem since you have a right triangle formed by Clarksville, Sparrowtown, and the airport. Here's how you can do it:

Clarksville is 54 miles due north of the airport.

Sparrowtown is due east of the airport, which forms the horizontal side of the right triangle.

The distance between Clarksville and Sparrowtown is 90 miles, which forms the hypotenuse of the right triangle.

Using the Pythagorean theorem:

a² + b² = c²

Where:

a is the distance from the airport to Clarksville (54 miles).

b is the distance from the airport to Sparrowtown (what we want to find).

c is the distance between Clarksville and Sparrowtown (90 miles).

Plug in the values:

54² + b² = 90²

Now, calculate:

2916 + b² = 8100

Subtract 2916 from both sides to isolate b²:

b² = 8100 - 2916

b² = 5184

Now, take the square root of both sides to find b:

b = √5184

b = 72

Answer 2

To find the distance between Sparrowtown and the airport, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the airport is the right angle, Clarksville is 54 miles due north (which we can call side A), and Sparrowtown is due east (which we can call side B). The distance between Clarksville and Sparrowtown is 90 miles (which we can call the hypotenuse, side C).

To find side B, we can use the following equation:

B^2 = C^2 - A^2

B^2 = 90^2 - 54^2

B^2 = 8100 - 2916

B^2 = 5184

Taking the square root of both sides gives us:

B = sqrt(5184)

B = 72

Therefore, Sparrowtown is [72] miles away from the airport.

Explanation:

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