Question

barry wants to measure the length of his ladder, but he doesnt have a long enough tape measure. instead, he leans the ladder up against a wall which he knows to be of height 2.4 m. he measures that the bottom of the ladder rests at a distance of 1.8 m away from the wall. find the length x of the ladder, in meters.

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, \(a = 1.8\) (distance from the wall), \(b=2.4\) (height of the wall), and \(c=x\) (length of the ladder). So, \(x^{2}=1.8^{2}+2.4^{2}\).

Step2: Calculate the squares

\(1.8^{2}=3.24\) and \(2.4^{2}=5.76\). Then \(x^{2}=3.24 + 5.76\).

Step3: Sum the values

\(3.24+5.76 = 9\). So, \(x^{2}=9\).

Step4: Solve for \(x\)

Take the square root of both sides. Since \(x>0\) (length), \(x=\sqrt{9}\).

Answer:

\(3\)