Question

A building casts a 185 foot shadow when the sun is at an angle of elevation of 45 degrees, what is the height of the building ?

Answer 1

For this case we can model the problem as a rectangle triangle where we have:
 Base of the triangle
 Angle between the base and the hypotenuse of the triangle
 We want to find:
 The height of the triangle
 For this, we use the following trigonometric relationship:
 $tan (45) = h / 185$
 Clearing the height we have:
 $h = 185 * tan (45) h = 185 feet$
 Answer:
 the height of the building is:
 h = 185 feet

Answer 2

See the attached picture to better understand the problem

we know that
in the right triangle ABC
tan 45°=BC/AC----> BC=AC*tan 45°----> BC=185*tan 45°---> BC=185 ft

the answer is
the height of the building is 185 ft