Question

nick has a 50-foot ladder. he places the ladder 20 feet away from the base of a building. what is the distance between the base of the building and the tip of the ladder, x, to the nearest foot?

Explanation:

Step1: Identify the triangle type

This is a right triangle problem, so we use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse (ladder, 50 ft), \(b\) is the base (20 ft), and \(a\) is the height (\(x\)).

Step2: Rearrange the formula

We solve for \(a\): \(a = \sqrt{c^2 - b^2}\)

Step3: Substitute values

Substitute \(c = 50\) and \(b = 20\) into the formula: \(a = \sqrt{50^2 - 20^2}\)

Step4: Calculate the values

First, calculate \(50^2 = 2500\) and \(20^2 = 400\). Then, \(2500 - 400 = 2100\). So, \(a = \sqrt{2100}\)

Step5: Approximate the square root

\(\sqrt{2100} \approx 45.83\), which rounds to 46.

Answer:

46