Question

1. two flag posts of height 5 m and 10 m are erected 13 m apart. find l, the length of the string (in meters) needed to join the tops of the two posts, correct to one decimal place.

Explanation:

Step1: Find the vertical distance between the tops of the two flag - posts

The vertical distance \(h\) between the tops of the two flag - posts is \(10 - 5=5\)m. The horizontal distance \(b = 13\)m.

Step2: Apply the Pythagorean theorem

According to the Pythagorean theorem \(l=\sqrt{h^{2}+b^{2}}\). Substitute \(h = 5\) and \(b = 13\) into the formula: \(l=\sqrt{5^{2}+13^{2}}=\sqrt{25 + 169}=\sqrt{194}\).

Step3: Calculate the value of \(l\)

\(\sqrt{194}\approx13.9\) (rounded to one decimal place)

Answer:

\(13.9\)