We can compare this problem to a puthagreom therom problem. We will be using the formula a^2+b^2=c^2
So we know that the trees hight a, and the the grounds distance b, form a right angle with the ropes legnth, c.
Since there is a 45 degree angle, and there is a right angle, 90 degrees, we add these together and subtract them from 180 since a triangle has a total of 180 degrees through its 3 angles. This gets us 45 degrees.
From that we know that a and b will be equal, since their angles are equal.
We put the values we know into the equation to get a^2+b^2=100^2=10,000
Since a and b are equal, we can simplify to get 2*(a^2)=10,000
Divide both sides by 2 to get a^2=5000
Find the square root of both sides to get a equals the square root of 5000.
The top of the treehouse is at the square root of 5000 feet, rounded to the nearest 10th of a foot, is 70.7 feet.
Hope this helps!
Oh and this isnt geometry/trig this is pre-algebra