Thread: Two Tricky Geometry Questions

1.) At 4 p.m on a certain day, the sun forms an angle of 18 degrees with the horizontal, shining for due west. How close to a house 20 feet high must a tree 30 feet high be to shade the west side of the house all the way to the top at this time?

2.) You have probably seen and used the fact that if the sum of the digits of an integer is divisible by 3, then the integer is divisible by 3. Prove this fact.

Thank you for your help in advance

1) When the shadow of the top of the tree touches the top of the house, tan(18) = (30 - 20)/d, where d is the distance between the tree and the hoouse.

2) If x ansd y are the digits in a number, then the intege is 10x + y or 10y + x. If x+y is divisible by 3, then (10x + y ) = ( 9x + x + y ) is also divisible by 3.

Thank you very much for your help. I had a feeling this is where i should have been going with #1 but I just wanted to make sure. Thank you very much I truly appreciate it