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

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

Answer 2

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