Question

a piece of lumber cut to support the treads of a stair as shown in the figure is called a stringer. find the length, ab, of the piece of lumber required for the stringer. 172.7 cm 121.9 cm

Explanation:

Step1: Identify the right - angled triangle

The vertical height \(AC = 172.7\) cm and the horizontal length \(BC=121.9\) cm. The length \(AB\) is the hypotenuse of a right - angled triangle \(ABC\).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - angled triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\). Here, \(a = 172.7\) and \(b = 121.9\), so \(AB=\sqrt{172.7^{2}+121.9^{2}}\).
First, calculate \(172.7^{2}=172.7\times172.7 = 29825.29\) and \(121.9^{2}=121.9\times121.9 = 14859.61\).
Then, \(172.7^{2}+121.9^{2}=29825.29 + 14859.61=44684.9\).
Finally, \(AB=\sqrt{44684.9}\approx211.4\) cm.

Answer:

\(211.4\) cm