Question

Wildgrove is 7 miles due north of the airport, and Yardley is due east of the airport. If the distance between Wildgrove and Yardley is 9 miles, how far is Yardley from the airport? If necessary, round to the nearest tenth.

Please respond soon.
Use the Pythagorean theorem.
Thank you!

Answer 1

5.7 miles

Explanation:

To find:-

• The distance between airport and Yardley.

Answer:-

We are given that airport and Wildgrove are 7miles apart and the distance between Yardley and Wildgrove is 9miles . We are interested in finding out tge distance between Yardley and airport.

As you can see from the figure attached, the distance can be calculated using Pythagoras theorem ,

`\rm\implies a^2+b^2 = h^2 \\`

where ,

• h is the longest side of the triangle (hypotenuse).
• a and b are two other sides .

Here the longest side is 9 miles and one other side is 7 miles . On substituting the respective values, we have;

`\rm\implies a^2 + (7)^2 = 9^2 \\`

`\rm\implies a^2 + 49 = 81 \\`

`\rm\implies a^2 = 81 - 49 \\`

`\rm\implies a^2 = 32 \\`

`\rm\implies a =√(32) \\`

`\rm\implies a = 5.65 \\`

`\rm\implies \red{ a = 5.7 } \\`

Hence the distance between Yardley and airport is 5.7 miles .

Answer 2

Yardley is approximately 5.7 miles away from the airport.

Explanation:

Let's use the following variables:

x = distance between Yardley and the airport

Using the Pythagorean theorem:

x^2 + 7^2 = 9^2

x^2 + 49 = 81

x^2 = 32

x = sqrt(32)

x ≈ 5.7

Therefore, Yardley is approximately 5.7 miles away from the airport.