Colton's school is due west of his house and due south of his friend Anthony's house. The distance between the school and Anthony's house is 4 miles and the straight-line distance between Colton's house and Anthony's house is 9 miles. How far is Colton's house from school? If necessary, round to the nearest tenth. miles
Question
Colton's school is due west of his house and due south of his friend Anthony's house. The distance between the school and Anthony's house is 4 miles and the straight-line distance between Colton's house and Anthony's house is 9 miles. How far is Colton's house from school? If necessary, round to the nearest tenth. miles
Solution
This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Here, we can consider the three locations (Colton's house, the school, and Anthony's house) as forming a right triangle. The distance between Anthony's house and the school is one side of the triangle (4 miles), the distance between Anthony's house and Colton's house is the hypotenuse (9 miles), and the distance between Colton's house and the school is the remaining side, which we'll call x.
According to the Pythagorean theorem:
(4 miles)^2 + x^2 = (9 miles)^2
16 miles^2 + x^2 = 81 miles^2
Subtract 16 miles^2 from both sides to isolate x^2:
x^2 = 81 miles^2 - 16 miles^2
x^2 = 65 miles^2
Finally, take the square root of both sides to solve for x:
x = sqrt(65 miles^2)
x ≈ 8.1 miles
So, Colton's house is approximately 8.1 miles from the school.
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