If Jack's house is 7.1 miles due north of the Senior Citizen Center and Belinda's house is 6.3 miles due west of it, then to the nearest tenth,what is the shortest distance between their houses?
You're looking for the hypotenuse of a right triangle.
Pythagorean Theorem:
a^2 + b^2 = c^2
7.1^2 + 6.3^2 = c^2
50.41 + 39.69 = c^2
90.1 = c^2
9.5 = c
To find the shortest distance between Jack's and Belinda's houses, we can use the Pythagorean theorem. The Pythagorean theorem 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.
In this case, we can imagine a right triangle with Jack's house at one vertex, Belinda's house at another vertex, and the Senior Citizen Center at the third vertex. The distance between Jack's and Belinda's houses is the hypotenuse of this triangle, while the distances to the Senior Citizen Center form the other two sides.
So, let's calculate the distance using the Pythagorean theorem:
Distance^2 = (Distance from Jack's house to Senior Citizen Center)^2 + (Distance from Belinda's house to Senior Citizen Center)^2
Distance^2 = (7.1 miles)^2 + (6.3 miles)^2
Distance^2 = 50.41 + 39.69
Distance^2 = 90.1
Taking the square root of both sides gives us:
Distance = √90.1
To the nearest tenth, the shortest distance between their houses is approximately 9.5 miles.