Question

Clint is a 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-$4$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?

Short answer

The solution is$7.65$feet.

Step-by-step solution

Step 1. Given information 

Each supporting end of the swing set is to be an A-frame constructed with two $10$foot long $4$-by-$4$joined at a $45°$angle.

Step 2. Calculation 

Let the joint between two$10$foot long 4-by-4 be A, the footings for each A-frame be B and C.

Now, $a^2=b^2+c^2-2bc\cos A$

$={10}^2+{10}^2-2\times 10\times 10\cos 45°$

$=100+100-200\cos 45°$

$a\approx 7.65$

So, the footings for each A-frame should be$7.65$feet apart.