Chapter 8.3, Problem 53AYU

To determine

How far apart should the footings for each A-frame be?

Answer to Problem 53AYU

  $\boxed{7.65feet}$

Explanation of Solution

Given information:

Clint is building a wooden swing set for his children. Each supporting end of the swing set is to be an A-frame constructed with two 10-foot-long 4-by-4s joined at a $45°$ angle. To prevent the swing set from tipping over, Clint wants to secure the base of each A-frame to concrete footings. How far apart should the footings for each A-frame be?

Calculation:

Let the distance between the supporting ends be $x$ .

The A-frame can be considered as an SAS triangle with two sides and the includede angle given. So, the Law of Cosines can be used to find the distance between the supporting ends.

  $x^2={10}^2+{10}^2-\mathrm{2.10.10.}\cos 45°$

  $=100+100-141.42$

  $=58.58$

Take square root on both the sides.

  $\sqrt{x^2}=\sqrt{58.58}$

  $x\approx 7.65$

Hence, the footing should be about $\boxed{7.65feet}$ apart.