SOLUTION: From the top of a 500m tall building the angle of depression to the top of another small building is 40 degrees and to the base of the smaller building is 50 degrees. 1. Find the

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Question 180121: From the top of a 500m tall building the angle of depression to the top of another small building is 40 degrees and to the base of the smaller building is 50 degrees.
1. Find the horizontal distance between the buildings.
2. Find the height of the smaller building.
Answer by Mathtut(3670) About Me  (Show Source):
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From the top of a 500m tall building the angle of depression to the top of another small building is 40 degrees and to the base of the smaller building is 50 degrees.
1. Find the horizontal distance between the buildings.
2. Find the height of the smaller building.
:
1)from the top of the tall building to the base of the small building a 40 degree angle is formed with respect to the tall building
:
so sin 40 = x/500....where x is the horizontal distance between buildings
:
.643=x/500--->x=321.5 feet
:
2) we also know that the angle formed to the top of the small building with respect to the tall building is 50 degrees so we can figure out the distance of where that line comes in contact with the ground.
:
sin 50=z/500
:
.766=z/500--->z=383 feet
:
now if we subtract those two distances 383-321.5=61.5 feet . now as you stand where that 383 foot line ends(on the ground) and look back up at the top of the tall building that also forms a 50 degree angle with respect to the ground. We are looking for the opposite side(height of small building). we have the angle and the adjacent side 61.5
:
sin 50 =h/61.5
:
.766=h/61.5--->h=47.11 feet (height of the small building)