Question

Dylan is hiking. He can either take a short cut up a steep flight of stairs or he can take the longer, flatter switchback route. If he goes on the switchback, he first travels west 60 meters and then turns and travels north 80 meters. Calculate the length in meters of the short cut up the flight of stairs. Round your answer to the nearest tenth.

Answer 1

We can use the Pythagorean theorem to find the length of the short cut up the flight of stairs. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's call the length of the short cut "x". Then, we can set up the following equation:

x^2 = 60^2 + 80^2

Expanding the squares:

x^2 = 3600 + 6400

x^2 = 10000

Taking the square root of both sides:

x = sqrt(10000)

x = 100

So, the length of the short cut up the flight of stairs is 100 meters.