Question

modeling with mathematics the fire escape forms a right triangle, as shown. use the pythagorean theorem to approximate the distance between the two platforms. round your answer to the nearest tenth. the distance is about \\(\square\\) feet.

Explanation:

Step1: Identify triangle sides

Assume the right triangle has legs \(a = 8.9\) ft and \(b = 15.7\) ft (from the image). Let the distance between platforms be the hypotenuse \(c\).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \(c = \sqrt{a^2 + b^2}\). Substitute \(a = 8.9\) and \(b = 15.7\):
\(a^2 = 8.9^2 = 79.21\), \(b^2 = 15.7^2 = 246.49\).
Sum: \(79.21 + 246.49 = 325.7\).
Then \(c = \sqrt{325.7} \approx 18.0\) (rounded to nearest tenth).

Answer:

18.0