A10 foot ladder is leaning against a building. the ladder makes a 45 degree angle with the building. how far up the building does the ladder reach

The answer is 5sqrt2 or 7.07
Since you have one 45 degree angle the other angle is also 45 degrees. This gives you a right isosceles triangle.
This can be solved using Pythagorean theorem or trig ratios.
a^2+a^2= 100
2a^2 = 100
a^2=50
a= sqrt 50
a=5sqrt2