Clint is building a wooden swing set for his children Each s

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-Iong 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? Therefore, the footings should be about feet apart. Round to two decimal places as needed.)

Solution

the support forms a triangle

whose 2 sides are 10 feet and included angle = 45 degrees

so applying law of cosines to find the distance between footings

x^2 = 10^2 + 10^2 - 2 (10) (10) cos 45

x = sqrt (100 + 100 - 200 cos 45 )

x = 7.65 feet

so , footings must be about 7.65 feet apart