apex angle of 2 8 foot 4x4's that are 62 inches apart at the bottom.

[jeep1965]

I'm trying to figure out the apex angle of 2 8 foot 4x4's that are 62 inches apart at the bottom.

 

[Quaid]

I'm trying to figure out the apex angle of two 8-foot 4x4s that are 62 inches apart at the bottom.

Hi Jeep:

Is this a homework exercise?

Is the 62" an inside measurement, as shown below?

Cheers :cool:


NOT TO SCALE

 

[jeep1965]

Apex angle?

Quaid Thank you for your reply! Your diagram is correct for the bottom but what I'm trying to figure out for the top is what degree the 4x4's need to be cut to lay flat together. Maybe "apex angle" isn't the correct terminology. Thank you for your help!

 

[HallsofIvy]

You can use the "cosine law": if a, b, and c are the lengths of sides of a triangle and C is the angle opposite side c, then \(\displaystyle c^2= a^2+ b^2- 2ab cos(C)\). Here, you can take a= b= 96 and c= 62 so this becomes \(\displaystyle 62^2= 96^2+ 96^2- 2(96)(96)cos(C)\) or \(\displaystyle 3844= 9216+ 9216- 18432 cos(C)\) which gives \(\displaystyle cos(C)= 0.79145\). The angle you need to cut is half of C.

 

[jeep1965]

Apex angle?

Denis thank you for your help! I finally got it figured out and no I'm not a student this is for a home project. Thanks again!:grin: