Percy's school is due west of his house and due south of his friend Ryan's house. The distance between the school and Ryan's house is 3 kilometers and the straight-line distance between Percy's house and Ryan's house is 5.3 kilometers. How far is Percy's house from school? If necessary, round to the nearest tenth.

Question

Percy's school is due west of his house and due south of his friend Ryan's house. The distance between the school and Ryan's house is 3 kilometers and the straight-line distance between Percy's house and Ryan's house is 5.3 kilometers. How far is Percy's house from school? If necessary, round to the nearest tenth.

Answer 1

Let 𝑎 be the distance between Ryan's house and the school, and 𝑏 be the distance between Percy's house and the school.

We can form a right triangle by connecting Percy's house, the school, and Ryan's house.
Using the Pythagorean theorem, we have 𝑏^2 + 𝑎^2 = 5.3^2 (1)
Also, 𝑎^2 − 𝑏^2 = 3^2 (2)
Adding equations (1) and (2), we get
𝑏^2 + 𝑎^2 + 𝑎^2 − 𝑏^2 = 5.3^2 + 3^2
2𝑎^2 = 28.09 + 9
2𝑎^2 = 37.09
𝑎^2 = 37.09 / 2
𝑎^2 ≈ 18.545
𝑎 ≈ √18.545 ≈ 4.3 (rounded to the nearest tenth)
Substituting 𝑎 = 4.3 back into equation (2), we get
4.3^2 − 𝑏^2 = 9
18.49 − 𝑏^2 = 9
𝑏^2 = 18.49 − 9 = 9.49
𝑏 ≈ √9.49 ≈ 3.1 (rounded to the nearest tenth)
Therefore, Percy's house is about 3.1 kilometers away from school. Answer: \boxed{3.1}.

Answer 2

To find the distance between Percy's house and the school, we can use the Pythagorean theorem. Let's call the distance between Percy's house and the school "x".

Using the Pythagorean theorem, we have:
x^2 = (3 km)^2 + (5.3 km)^2

Simplifying, we get:
x^2 = 9 km^2 + 28.09 km^2
x^2 = 37.09 km^2

Taking the square root of both sides, we have:
x = √37.09 km

Rounding to the nearest tenth, Percy's house is approximately 6.1 km from the school.

Answer 3

To find the distance between Percy's house and school, we can use the Pythagorean theorem. Since the school is due west of Percy's house and due south of Ryan's house, we can create a right triangle where the distance between Percy's house and the school is the hypotenuse, the distance between Percy's house and Ryan's house is one leg, and the distance between Ryan's house and the school is the other leg.

Let's call the distance between Percy's house and the school "x" kilometers. Using the Pythagorean theorem, we can set up the following equation:

x^2 = (3 km)^2 + (5.3 km)^2

Simplifying, we get:

x^2 = 9 + 28.09
x^2 = 37.09

To find x, we need to take the square root of both sides of the equation:

x = √37.09

Calculating the square root, we find that x is approximately equal to 6.1 kilometers. Therefore, Percy's house is approximately 6.1 kilometers away from his school.