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

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:
 
 Clearing the height we have:
 
 
 the height of the building is:
 h = 185 feet

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

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